Sound Wave Equation Research Articles

An Investigation on Numerical Simulation Method for Aero-Acoustics Based on Acoustics Analogy

A numerical simulation method on noise prediction, which incorporates aerodynamics and sound wave equations based on acoustic analogy, is presented in the paper. Near-field unsteady aerodynamic characteristic can be obtain by large eddy simulation (LES), and far-field propagation of sound waves and spatial sound-field can be obtain by solving the time-domain integral equations of Ffowcs Williams and Hawings (FW-H). Based on the method, a numerical simulation was done on a two-dimension cylinder and a three-dimension flat plate with blunt leading edge. The agreement of numerical results with experiment data validated the Feasibility of the method. The results also indicate that LES can describe vortex generation and shedding in the flow-fields, and FW-H formulation, which has taken time-lag between sound emission and reception times into account, can simulate time-effect of sound propagation toward far-fields.

An Investigation on Numerical Simulation Method for Aero-Acoustics Based on Acoustics Analogy

A numerical simulation method on noise prediction, which incorporates aerodynamics and sound wave equations based on acoustic analogy, is presented in the paper. Near-field unsteady aerodynamic characteristic can be obtain by large eddy simulation (LES), and far-field propagation of sound waves and spatial sound-field can be obtain by solving the time-domain integral equations of Ffowcs Williams and Hawings (FW-H). Based on the method, a numerical simulation was done on a two-dimension cylinder and a three-dimension flat plate with blunt leading edge. The agreement of numerical results with experiment data validated the Feasibility of the method. The results also indicate that LES can describe vortex generation and shedding in the flow-fields, and FW-H formulation, which has taken time-lag between sound emission and reception times into account, can simulate time-effect of sound propagation toward far-fields.

The numerical simulation of propagation of intensive acoustic noise

The propagation of intensive acoustic noise is of fundamental interest in nonlinear acoustics. Some of the simplest models describing such phenomena are generalized Burgers’ equations for finite amplitude sound waves. An important problem in this field is to find the wave’s behavior far from the emitting source for stochastic initial waveforms. The method of numerical solution of generalized Burgers equation proposed is step-by-step calculation supported on using Fast Fourier Transform of the considered signal. The general idea is to keep only Fourier image of concerned signal and update it recursively (in space). For simulating the wave evolution we used 4096 (212) point realizations and took averaging over 1000 realizations. Also the object of the present study is a numerical analysis of the spectral and bispectral functions of the intense random signals propagating in nondispersive nonlinear media. The possibility of recovering the input spectrum from the measured spectrum and bispectrum at the output of the nonlinear medium is discusses. The analytical estimations are supported by numerical simulation. For two different types of primary spectrum evolution of jet noise were numerically simulates at a short distance and assayed bispectrum and a spectrum analysis of the signals.

Investigation of sound scattering by a surface using the acoustical wave propagator method

The time domain acoustical wave propagator (AWP) method is used as a tool to study the sound scattering properties of a surface. As the method allows the modeling of the excitation, absorption, and scattering of sound in a vicinity of the surface within a very short period of time, the effect of other surfaces on these process can be ignored, and the acoustical property of a specific surface can be investigated in detail without solving the sound wave equation in the whole space. Sound scattering by a finite impedance strip mounted on a rigid baffle in two different conditions is solved by the method. The result is used to illustrate the efficiency of the method.

Research on Piezoelectric Transducer with Negative Impedance by FEM

Piezoelectric transducer with negative impedance matching circuit is put forward to enhance its performance in broadband frequencies. The typical multi-physics problem is coupled with sound wave equations, structure stress-strain equations, piezoelectric constitutive equations and electric ordinary equations, and it is analyzed with FEM in detail. Frequency response characteristics are simulated when shunted with negative-impedance in series. When proper negative synthesized elements are connected, the performance of low frequencies and bandwidth are enhanced obviously.

Nonlinear bubble dynamics of cavitation

A theoretical framework for studying cavitation dynamics is revived. It consists of a nonlinear sound wave equation in an acoustic cavitation environment together with the bubble motion equation. The nonlinear sound wave equation considers time delayed bubble-bubble interaction. For cavitation clouds generated in a standing sound wave driven by an ultrasonic horn, the equations are numerically solved under an approximation. It is found that the number density of bubble is a key parameter in describing the bubble dynamics of cavitation. Adjusting this parameter, our calculation may produce the chaotic acoustic pressure and various different forms of bubble motion in cavitation cloud, and can qualitatively reproduce experimentally observed phenomena.

Comparison of cavitational activity in different configurations of sonochemical reactors using model reaction supported with theoretical simulations

The present work deals with evaluation of different configurations of sonochemical reactors using a model reaction with justification on the basis of cavitational activity predictions of theoretical simulations. In addition, intensification of the cavitational effects using additives has been investigated and its dependency on the inherent cavitational activity in the reactor has been established. The model reaction used for experimental investigations is the potassium iodide oxidation, also known as the Weissler reaction whereas the theoretical prediction of cavitational activity has been achieved using the numerical simulations of the sound wave equation using Comsol Multi physics software. The effects of various additives for enhancing the cavitational activity such as solid particles like cupric oxide, salts like sodium nitrite and radical promoters such as ferrous sulphate have also been investigated. It has been observed that the configuration with higher transducer areas gives better distribution of the cavitational activity and also gives enhanced effects as quantified using the cavitational yield measurements. Also it has been conclusively established that depending on the mechanism of intensification, the beneficial effects obtained using different additives are strongly dependent on the inherent cavitational activity which in turn depends on the type of reactor and the operating conditions.

A lattice Boltzmann model for two‐dimensional sound wave in the small perturbation compressible flows

AbstractA multi‐entropy‐level lattice Boltzmann model for two‐dimensional sound wave equation in the small perturbation flows is presented. In this model, we used higher‐order moment method, multi‐scale technique and the Chapman–Enskog expansion, and multi‐entropy‐level to obtain sound wave equation with isentropic equation. As numerical examples, the Doppler effects in the sound wave propagation, the sound scattering from circular cylinder are simulated. The numerical results show that this model can be used to simulate sound wave propagation. Copyright © 2010 John Wiley & Sons, Ltd.

Analysis of Piezoelectric Acoustic Sensor Based on Negative Impedance with FEM in Composite Materials

Piezoelectric acoustic sensor with negative impedance matching circuit is put forward to enhance its sensitivity at low frequencies. The multi-physics problem coupled with sound wave equations, structure stress-strain equations, piezoelectric constitutive equations and electric ordinary equations is analyzed with FEM in detail. Frequency response characteristics are simulated when shunted with negative-capacitance, resistance in series. Sensitivity is obtained from 1kHz to 5kHz. When used proper electrical elements, the sensitivity of the piezoelectric sensor can even exceed that of no matching circuit over 2 factors in broad band.

Ultrasound and vortex oscillations in high-temperature superconductors

An HTSC powder sample with grain (particle) diameter of 20–50 μm placed in a dc magnetic field B0 and cooled to a temperature below the superconducting transition temperature was exposed to the radiofrequency (rf) pulsed magnetic field B∼ (B∼ ⊥ B0) at a carrier frequency of 30.7 MHz. Stable echo signals were recorded which followed different rf-pulse trains. This phenomenon has the following mechanism. The rf magnetic field stimulates fluxoid oscillations on the HTSC grain surface, which are transformed into lattice oscillations through the pinning centers and induce a propagating sound wave. The second-order nonlinearity with respect to the gradient of the crystal lattice deviation from the equilibrium position taken into account in the sound wave equation yields the dependence of the crystal lattice natural frequency on the amplitude and length of the pulses which excite these oscillations. This dependence is responsible for the emergence of echo signals.

Nonlinear theory of ionic sound waves in a hot quantum-degenerate electron-positron-ion plasma

A collisionless nonmagnetized e-p-i plasma consisting of quantum-degenerate gases of ions, electrons, and positrons at nonzero temperatures is considered. The dispersion equation for isothermal ionic sound waves is derived and analyzed, and an exact expression is obtained for the linear velocity of ionic sound. Analysis of the dispersion equation has made it possible to determine the ranges of parameters in which nonlinear solutions in the form of solitons should be sought. A nonlinear theory of isothermal ionic sound waves is developed and used for obtaining and analyzing the exact solution to the system of initial equations. Analysis has been carried out by the method of the Bernoulli pseudopotential. The ranges of phase velocities of periodic ionic sound waves and soliton velocities are determined. It is shown that in the plasma under investigation, these ranges do not overlap and that the soliton velocity cannot be lower than the linear velocity of ionic sound. The profiles of physical quantities in a periodic wave and in a soliton are constructed, as well as the dependences of the velocity of sound and the critical velocity on the ionic concentration in the plasma. It is shown that these velocities increase with the ion concentration.

COMPUTATION OF THE FLOW AND NEAR SOUND FIELDS OF A FREE SURFACE PIERCING CYLINDER

The near sound field generated due to a vertically mounted circular cylinder piercing a free surface in shallow water, is studied computationally using the Large Eddy Simulation (LES) approach and the sound wave equation. The flow is simulated in both the air and water phases. The interface surface is allowed to move and is simulated using the Volume of Fluid technique. The pressure distribution over the cylinder is fed back into the sound wave equation to calculate the near field. The interface surface is modeled as a zero pressure surface in the acoustic calculation and the bottom is taken as having infinite impedence modeling the case of a rigid floor. Two of acoustic calculations methods are used. In the first method, the interface surface is assumed to be fixed and the wave equation is solved in the frequency domain in a post-processing stage. In the second method, the evolution of the interface surface is taken into account and the wave equation is simulated simultaneously with the LES. Both solutions are analyzed and compared to show that the interface surface acts as a strong damper to the low frequency sound by damping the vortex Von Karman rollers as well as causing the low frequency component to be nonradiative. The variation of the near sound field with the water depth and Froude number is investigated and the propagation and damping characteristics are analyzed.

Wave equations arising from perturbations of Bianchi III manifolds

We perform a linear perturbation study of two instances of Bianchi III manifolds: dust and radiation. We take the metric approach and perturb the metric component by component. Once we construct gauge-invariant variables we work without fixing the gauge and use the perturbations as ingredients of the gauge-invariant equations that result when the field equations are enforced to first order. Exact solutions to gauge-invariant equations are extracted explicitly. When possible, we rewrite our solutions as wave equations, giving the evidence of gravitational radiation and sound waves. In total, we list four gravitational wave equations, three sound wave equations and one equation coupling a gravitational wave to a sound wave. These resonances are not at all independent and we point out some identities. Some late-time behaviour is discussed. The approach is wholly general; the resulting equations are physically relevant and informative.

Comment on “Sound velocity and multibranch Bogoliubov spectrum of an elongated Fermi superfluid in the BEC-BCS crossover”

The work by T. K. Ghosh and K. Machida [cond-mat/0510160 and Phys. Rev. A 73, 013613 (2006)] on the sound velocity in a cylindrically confined Fermi superfluid obeying a power-law equation of state is shown to make use of an improper projection of the sound wave equation. This inaccuracy fully accounts for the difference between their results and those previously reported by Capuzzi et al. [cond-mat/0509323 and Phys. Rev. A 73, 021603(R) (2006)]. In this Comment we show that both approaches lead exactly to the same result when the correct weight function is used in the projection. Plots of the correct behavior of the phonon and monopole-mode spectra in the BCS, unitary, and BEC limits are also shown.

On the necessity of non-Riemannian acoustic spacetime in fluids with vorticity

The necessity of a newly proposed [L.C. Garcia de Andrade, Phys. Rev. D 70 (2004) 64004] non-Riemannian acoustic spacetime structure called acoustic torsion of sound wave equation in fluids with vorticity are discussed. It is shown that this structure, although not always necessary is present in fluids with vorticity even when the perturbation is rotational. This can be done by solving the Bergliaffa et al. [Physica D 191 (2004) 121] gauge invariant equations for sound, superposed to a general background flow, needs to support a non-Riemannian acoustic geometry in effective spacetime. Bergliaffa et al. have previously shown that a Riemannian structure cannot be associated to this gauge invariant general system.

Acoustic Instability in Inhomogeneous Gas-Discharge Plasma

The possibility of amplification of acoustic waves in inhomogeneous atomic dc gas-discharge plasma (positive column of glow discharge) is investigated theoretically. This amplification is caused by the transfer of thermal energy from electrons to colder electron gas under conditions of elastic electron-atom collisions. It is demonstrated that the inclusion of nonuniform distribution of equilibrium temperature, neutral gas concentration, and electron concentration over the plasma column cross section, similar to the case of uniform distribution, cannot result in acoustic instability and, consequently, in the interpretation of the experimental results in sound amplification in weakly ionized plasma. The dispersion equation for sound waves in inhomogeneous glow-discharge plasma is derived and numerically analyzed in detail. Comparison of the theoretical and experimental results enables one to identify the reasons for their discrepancy and to actually reveal the basic principles essential for constructing a theory which will make it possible to quantitatively and adequately describe the experimental data on the amplification of sound in weakly ionized atomic plasma.

A study of the band structure in two-dimensional phononic crystals based on plane-wave algorithm

In this paper, the calculating course of the plane-wave algorithm is introducedto solve the sound wave equation and the band structure of phononic crystals. The phononic crystals of two-dimensional binary liquid systems are studied. In conclusion, the CCl4/mercury system is easier to obtain the band-gap than the mercury/CCl4 system. With the increase of the filling fraction(f), the width of the band-gap becomes wider and then narrower. The widest band-gap of CCl4/mercury system appears at f=0229,where ΔΩmax=0549.While the width of the band-gap in mercury/CCl4 system increases consistently with the filling fraction, when f=0.554,ΔΩmax=0515.Under the same filling fraction, the variation of the cylinder diameter and lattice constant does not affect the band-gap width ΔΩ.

Low-frequency models to compare acoustical performance of ducts of gradual area change

When two ducts of different circular cross-sectional area are joined together to form an acoustical transmission system, an additional impedance is introduced. This particular problem is found commonly in air conditioning systems among others. Simple models are used to solve the sound wave equation, and they assume that the plane wave mode is responsible for the most part of the transmission/insertion loss calculation. From previous works, it appears that, although higher-order modes can propagate at certain frequencies, their transmission efficiency is low and they do not cause a critical deviation from the assumption of one-dimensional propagation. The models are based on numerical/semi-analytical and asymptotic approximations to transform the sound pressure wave equation into an acoustic impedance equation with proper boundary conditions. The final aim is to calculate the transfer impedance of the duct section which can be used to calculate the sound field radiated. The model should be extended to ducts with incompressible mean flow for low flow Mach numbers, and further work is currently under progress on this subject. However, for low mean flow, the effect on the transmission loss has been found to be only marginal for some particular geometries. [Work supported by Fondecyt, Grant No. 1020196.]

Iordanskii force and the gravitational Aharonov-Bohm effect for a moving vortex

I discuss the scattering of phonons by a vortex moving with respect to a superfluid condensate. This allows us to test the compatibility of the scattering-theory derivation of the Iordanskii force with the Galilean invariance of the underlying fluid dynamics. In order to obtain the correct result we must retain ${O(v}_{s}^{2})$ terms in the sound-wave equation, and this reinforces the interpretation, due to Volovik, of the Iordanskii force as an analogue of the gravitational Bohm-Aharonov effect.

Relativistic acoustic geometry

Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field propagating in a curved spacetime geometry. The geometry is described by the acoustic metric tensor which depends locally on the equation of state and the 4-velocity of the fluid. For a relativistic supersonic flow in curved spacetime the ergosphere and acoustic horizon may be defined in a way analogous to the non-relativistic case. A general-relativistic expression for the acoustic analogue of surface gravity has been found.