Nonlinear Acoustic Model Research Articles

On the instability of single-axis acoustic levitation under radial perturbations

Acoustic levitation is widely used in non-container measurement and non-contact manipulation. Particles in the single-axis acoustic levitation are easily unstable in the radial direction under external perturbations. In order to explore the instability in the acoustic levitation during radial perturbations, a nonlinear acoustic levitation model considering the coupling of radial and axial vibration is proposed to analyze the dominant factors influencing the levitation stability, an acoustic levitation system consisting of a transducer and a plane reflector is established, and high-speed photography is used to observe the vibration behavior of the particle with large radial vibration and the levitation stability. The simulation results are compared and verified with the experiments, which indicate that the reduction in axial trapping stiffness due to radial vibration plays a vital role in the levitation instability. The present model can characterize the radial anti-interference ability of different levitators as well as predict the movement trajectories of levitated particles after being disturbed, which is helpful to optimize the design of acoustic levitators and provide guidance for acoustic manipulation.

Nonlinear supersonic flutter of a composite panel backed by an acoustic cavity with finite-amplitude sound waves

In this paper, an implicit partitioned fluid-structure-acoustic interaction method is presented for predicting nonlinear aeroelastic response of an elastic composite laminated panel backed by an acoustic cavity and subject to a supersonic flow. The method is formulated in an arbitrary Lagrangian-Eulerian framework based on the unsteady Navier-Stokes equations for the supersonic flow, a geometrical nonlinear dynamics model for the composite laminated panel, and the nonlinear Westervelt equation for the finite-amplitude sound waves in cavity. A theoretical fluid-structure-acoustic model of the supersonic panel is proposed for validating the present numerical method, in which the nonlinear structural model of the panel, the first-order piston aerodynamics model of the supersonic flow and the nonlinear sound wave model of the cavity are coupled in a monolithic manner. It is found that cavity acoustic resonance can appear in the case a vibration mode of the panel coalescing with an acoustic mode of the cavity. Several new physical features of nonlinear acoustic resonance have been discovered, such as the presence of shock wave with high pressure gradients travelling along the resonant cavity in axial direction and the presence of higher-order harmonic wave components, which emphasize a nonlinear acoustic wave model of the cavity must be used to fully characterize these phenomena. In addition, the nonlinearity of the standing wave is quantitatively related to the acoustic modes by means of a proper orthogonal decomposition analysis.

Improvement of micro-perforated panel absorbers sound performance using resistive screens and sensitivity analysis of the composite absorber models

The sound attenuation performance of a composite absorber constituted by a micro- perforated panel, a resistive screen that is inserted into the air cavity and a rigid back plate, is studied. Using a nonlinear acoustic impedance model, the surface impedance of the absorber is determined by transfer matrix method, and the models are validated by comparison with experimental measurements performed at different sound pressure levels up to 150 dB. The contribution of the resistive screens in improving the acoustic performances of micro-perforated panel absorbers is presented. It is shown that the resistive screen increases the resistance of the absorber resulting in broadening of the absorption frequency band and improvement of the absorption coefficient when an appropriate perforation ratio of the panel is used. Sensitivity analysis is performed at higher pressure excitations, and the dimensionless input parameters are the perforation ratio of the panel, the ratio of the perforation diameter by the thickness of the panel, the ratio of the cavity depth by the thickness, the orifice Mach number and the resistance per unit area of the screen. The analysis shows the impact of the input parameters on the normalized surface impedance and the sound absorption coefficient of the absorber. It is demonstrated that the resistance per unit area of the screen influences strongly the acoustic properties of the absorber in the linear regime, while the perforation ratio of the panel and the orifice Mach number are the dominant parameters which control the acoustic behavior of the absorber in the nonlinear regime.

Broadband quasi-perfect sound absorption by a metasurface with coupled resonators at both low- and high-amplitude excitations

This study presents an acoustic metasurface (AM) consisting of coupled Helmholtz resonators with extended necks (HRENs) to effectively absorb broadband sound waves at both low and high amplitudes. A nonlinear acoustic model is proposed to characterize the AM performance based on the equivalent medium theory and the transfer matrix method. The nonlinear effects due to the high-amplitude excitation are considered by a velocity-dependence equivalent density of the air in the neck. The acoustic characteristics of an AM with two coupled HREN units at the sound pressure level (SPL) ranging from 100dB to 140dB are analytically, numerically, and experimentally investigated. Results from the three approaches show good agreement. The AM achieves quasi-perfect absorption (absorption coefficient α>0.9) in a wide range of SPL, while each HREN unit alone only performs well at around 130dB. The superior absorption performance of the AM at relatively low-amplitude excitation originates from the coherent coupling effects between adjacent units. With the increase of the sound level, the coupling effects tend to deteriorate; fortunately, the sound-vortex conversions occur, contributing to additional acoustic dissipation and thereby sustaining the quasi-perfect absorption capability. Based on the absorption mechanisms, a broadband AM with multiple coupled resonators is designed and manufactured. The measured averaged absorption coefficient of the AM is larger than 0.91 at the SPL below 140 dB (α>0.97 at 100dB) within [700,1100]Hz, and the compact thickness is of 1/18 wavelength at the lowest operating frequency. The findings in this study offer a promising approach to achieve highly efficient broadband sound absorption in a wide-ranging noise level, which holds great potentials in practical applications for noise control.

A novel variational perturbation approach for formulating both linear and nonlinear acoustic model equations

A novel approach, based on variational principles, for obtaining linear acoustic model equations directly from an arbitrary Lagrangian is presented, followed by extension to the case of weakly nonlinear acoustics. The efficacy and ease of application of the methodology adopted is demonstrated for two different Lagrangians: one describing classical potential flow, the other relativistic flow including viscous dissipation. It is shown, following appropriate simplification, that corresponding classical, well-known wave equations available in the open literature, derived in the recognised standard manner, are recovered.

An arbitrary Lagrangian–Eulerian method for analyzing finite-amplitude viscous acoustic waves radiated from vibrational solid boundaries: An implicit method

This paper is concerned with the development of an arbitrary Lagrangian–Eulerian (ALE) method for predicting nonlinear acoustic waves radiated from large-amplitude vibrational solid boundaries immersed in viscous fluids of infinite extent. The method is formulated based on a nonlinear acoustic model characterized by velocity potential and acoustic pressure. Unsplit implementations of three perfectly matched layer (PML) techniques are presented, namely conventional PML, convolution PML, and complex frequency-shifted PML (CFS-PML), to enable bounded-domain modeling of nonlinear acoustic waves propagating in an unbounded fluid medium. The long-time stability characteristics of the three distinct PML techniques are examined through theoretical analysis and numerical verification of their ability to absorb evanescent waves. Our results reveal that the CFS-PML technique exhibits superior long-time stability performance compared to the other two techniques. The CFS-PML is also compared to two different absorbing layer techniques: the Kosloff Absorbing Layer (KAL) technique and the Acoustic Black Hole (ABH) technique. The finite element method is adopted for spatial discretization of the finite-amplitude acoustic wave model, and an implicit predictor–corrector algorithm is proposed for time advancement. Several benchmark problems, including acoustic waves produced by a vibrational piston, and transversely oscillating and pulsating cylinders, are analyzed by the proposed method. It is found that the proposed method attains a second-order rate of convergence for spatial discretization, and the convergence rate in terms of the time step size is about first-order. The application of the method to acoustic levitation problems is also demonstrated, and the nonlinear phenomenon of acoustic waves in a single-axis acoustic levitator is discussed.

An arbitrary Lagrangian-Eulerian method for nonlinear structural-acoustic interaction of hyperelastic solid and compressible viscous fluid

This paper develops a numerical method for predicting the nonlinear structural-acoustic interactions of a hyperelastic solid immersed in an unbounded compressible viscous fluid. The nonlinear acoustic wave model with perfectly matched layers adopted is proposed in an arbitrary Lagrangian-Eulerian frame to absorb acoustic waves at truncated fluid boundaries, whereas the geometric and material nonlinearities of the hyperelastic solid are characterized in a total Lagrangian form. Both the fluid and the solid are discretized by the finite element method, and both models are coupled together by the momentum equilibrium and kinematic compatibility on the common interface. The convergence and accuracy of the proposed method are assessed by comparing the computed results with existing solutions. A hyperelastic ring in a viscous fluid is analyzed to provide physical insights into the nonlinear dynamics behaviors of the coupled hyperelastic solid and acoustic fluid system. The hyperelastic ring in acoustic fluid exhibits deformation instability under a uniform distributed excitation load, producing a series of subharmonics, ultrasubharmonics, and superharmonics in the structural and acoustic responses. Nonlinear internal resonance and bifurcation phenomena in the vibration of the ring and the acoustic waves of the fluid are also discussed.

Modeling acoustic cavitation with inhomogeneous polydisperse bubble population on a large scale

A model for acoustic cavitation flows able to depict large geometries and time scales is proposed. It is based on the Euler–Lagrange approach incorporating a novel Helmholtz solver with a non-linear acoustic attenuation model. The method is able to depict a polydisperse bubble population, which may vary locally. The model is verified and analyzed in a setup with a large sonotrode. Influences of the initial void fraction and the population type are studied. The results show that the velocity is strongly influenced by these parameters. Furthermore, the largest bubbles determine the highest pressure amplitude reached in the domain, which corresponds to the Blake threshold of these bubbles. Additionally, a validation is performed with a small sonotrode. The model reproduces most of the experimentally observed phenomena. In the experiments, neighboring bubbles are found which move in different directions depending on their size. The numerical results show that the responsible mechanism here is the reversal of the primary Bjerknes force at a certain pressure amplitude.

Majors About the New Symmetry of a Nonlinear Acoustics Model

The Lie symmetry group of the Zabolotskaya-Khokhlov equation has been seriously studied, earlier than this. Eventually, it has been endowed with a general model by N.J.C. Ndogmo, in 2008. This research is devoted to introducing the algebra, the group, and the reductions of a new symmetry which is an exception of that model.

Parabolic Approximation of Quasilinear Wave Equations with Applications in Nonlinear Acoustics

This work deals with the convergence analysis of parabolic perturbations to quasilinear wave equations on smooth bounded domains. In particular, we consider wave equations with nonlinearities of quadratic type, which cover the two classical models of nonlinear acoustics, the Westervelt and Kuznetsov equations. By employing a high-order energy analysis, we obtain convergence of their solutions to the corresponding inviscid equations' solutions in the standard energy norm with a linear rate, assuming small data and a sufficiently short time. The smallness of initial data can, however, be imposed in a lower-order norm than the one needed in the energy analysis. It arises only from ensuring the nondegeneracy of the studied wave equations. In addition, we address the open questions of local well-posedness of the two classical models on bounded domains with a nonnegative, possibly vanishing sound diffusivity.

Nonlinear Waveform Inversion for Quantitative Ultrasound

Due to its non-invasive and non-radiating nature, along with its low cost, ultrasound (US) imaging is widely used in medical applications. Typical B-mode US images have limited resolution and contrast and weak physical interpretation. Inverse US methods were developed to reconstruct the media's speed-of-sound (SoS) based on a linear acoustic model. However, the wave propagation in medical US is governed by nonlinear acoustics, which introduces more complex behaviors neglected in the linear model. In this work we propose a nonlinear waveform inversion (NWI) approach for quantitative US, that considers a nonlinear acoustics model to simultaneously reconstruct multiple material properties, including the medium's SoS, density, attenuation, and nonlinearity parameter. We thus broaden current inverse US approaches, such as the full waveform inversion (FWI) algorithm, by considering nonlinear media, and additional physical parameters. We represent the nonlinear acoustic model by means of a recurrent neural network, which enables us to apply advanced optimization algorithms borrowed from the deep learning toolbox and achieve more efficient reconstructions compared to the FWI method. We evaluate the performance of our approach on in-silico data and show that neglecting nonlinear effects may result in substantial degradation in the reconstruction, paving the way of NWI into clinical applications.

An experimental validation of a nonlinear acoustic resistance model for an acoustically compact area contraction with steady mean flow.

In a previously published paper, a model for the nonlinear acoustic response of an area contraction including bias flow was presented. The model's prediction for the zero-driving resistance grew progressively worse as the steady-flow Mach number increased. This trend suggests that the forward loss coefficients should depend on the steady Mach number. This letter provides an empirical fitting of this Mach number dependence, along with additional validation data for the model. These additional validation data corroborate the model's prediction that the nonlinear impedance is frequency independent. This letter additionally provides an experimental methodology for determining the characteristic length with sample results.

Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

We relate together different models of non linear acoustic in thermo-elastic media as the Kuznetsov equation, the Westervelt equation, the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Nonlinear Progressive wave Equation (NPE) and estimate the time during which the solutions of these models keep closed in the \begin{document}$ L^2 $\end{document} norm. The KZK and NPE equations are considered as paraxial approximations of the Kuznetsov equation. The Westervelt equation is obtained as a nonlinear approximation of the Kuznetsov equation. Aiming to compare the solutions of the exact and approximated systems in found approximation domains the well-posedness results (for the Kuznetsov equation in a half-space with periodic in time initial and boundary data) are obtained.

The Jordan–Moore–Gibson–Thompson Equation: Well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time

In this paper, we consider the Jordan–Moore–Gibson–Thompson equation, a third-order in time wave equation describing the nonlinear propagation of sound that avoids the infinite signal speed paradox of classical second-order in time strongly damped models of nonlinear acoustics, such as the Westervelt and the Kuznetsov equation. We show well-posedness in an acoustic velocity potential formulation with and without gradient nonlinearity, corresponding to the Kuznetsov and the Westervelt nonlinearities, respectively. Moreover, we consider the limit as the parameter of the third-order time derivative that plays the role of a relaxation time tends to zero, which again leads to the classical Kuznetsov and Westervelt models. To this end, we establish appropriate energy estimates for the linearized equations and employ fixed-point arguments for well-posedness of the nonlinear equations. The theoretical results are illustrated by numerical experiments.

Sensitivity analysis of micro-perforated panel absorber models at high sound pressure levels

Sensitivity analysis is performed using a nonlinear acoustic impedance model of micro-perforated panel absorbers constituted by a micro-perforated panel bonded on a honeycomb structure in order to assess the impacts of the input parameters on the outputs of interest namely the normalized surface impedance and the sound absorption coefficient. The theoretical results predicted by the nonlinear impedance model show good agreement with experimental measurements performed at high sound pressure level using an impedance tube. The inputs of the model are the plate thickness, the orifice diameter, the perforation ratio, the cavity depth and the sound pressure level. For higher pressure levels excitations, it is demonstrated that the perforation ratio is the key parameter which affects significantly the resistance and the sound absorption of the absorber at the resonance while the impacts of the thickness and orifice diameter of the panel are negligible. In addition, the study confirms that the acoustic reactance is dominated by the cavity depth especially at low frequencies and the sound pressure level influences strongly the acoustic behaviour of micro-perforated panel absorbers. Therefore, the design of a micro-perforated panel absorber requires the knowledge of the sound pressure level and the perforation ratio control quality must be done carefully in order to get the target performances of the absorber.

Models of nonlinear acoustics viewed as an approximation of the Navier–Stokes and Euler compressible isentropic systems

The derivation of different models of non linear acoustic in thermo-ellastic media as the Kuznetsov equation, the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Nonlinear Progressive wave Equation (NPE) from an isentropic Navier-Stokes/Euler system is systematized using the Hilbert type expansion in the corresponding perturbative and (for the KZK and NPE equations) paraxial \textit{ansatz}. The use of small, to compare to the constant state perturbations, correctors allows to obtain the approximation results for the solutions of these models and to estimate the time during which they keep closed in the L² norm. In the aim to compare the solutions of the exact and approximated systems in found approximation domains a global well-posedness result for the Navier-Stokes system in a half-space with time periodic initial and boundary data was obtained.

Ultrasonic liquid metal processing: The essential role of cavitation bubbles in controlling acoustic streaming

The acoustic streaming behaviour below an ultrasonic sonotrode in water was predicted by numerical simulation and validated by experimental studies. The flow was calculated by solving the transient Reynolds-Averaged Navier-Stokes equations with a source term representing ultrasonic excitation implemented from the predictions of a nonlinear acoustic model. Comparisons with the measured flow field from Particle Image Velocimetry (PIV) water experiments revealed good agreement in both velocity magnitude and direction at two power settings, supporting the validity of the model for acoustic streaming in the presence of cavitating bubbles. Turbulent features measured by PIV were also recovered by the model. The model was then applied to the technologically important area of ultrasonic treatment of liquid aluminium, to achieve the prediction of acoustic streaming for the very first time that accounts for nonlinear pressure propagation in the presence of acoustic cavitation in the melt. Simulations show a strong dependence of the acoustic streaming flow direction on the cavitating bubble volume fraction, reflecting PIV observations. This has implications for the technological use of ultrasound in liquid metal processing.

Models of nonlinear acoustics viewed as an approximation of the Navier-Stokes and Euler compressible isentropic systems

The derivation of different models of non linear acoustic in thermo-ellastic media as the Kuznetsov equation, the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Nonlinear Progressive wave Equation (NPE) from an isentropic Navier-Stokes/Euler system is systematized using the Hilbert type expansion in the corresponding perturbative and (for the KZK and NPE equations) paraxial ansatz . The use of small, to compare to the constant state perturbations, correctors allows to obtain the approximation results for the solutions of these models and to estimate the time during which they keep closed in the L2 norm. The KZK and NPE equations are also considered as paraxial approximations of the Kuznetsov equation, which is a model obtained only by perturbations from the Navier-Stokes/Euler system. The Westervelt equation is obtained as a nonlinear approximation of the Kuznetsov equation. In the aim to compare the solutions of the exact and approximated systems in found approximation domains the well-posedness results (for the Navier-Stokes system and the Kuznetsov equation in a half-space with periodic in time initial and boundary data) were obtained.

High-intensity focused ultrasound (HIFU) ablation by frequency chirp excitation: reduction of the grating lobe in axial focus shifting

High-intensity focused ultrasound (HIFU) ablation has gained popularity in tumor treatment. However, the pre-focal heating due to the presence of the grating lobe may generate unintended heating in clinical applications and limit the steering abilities of the phased array design. In order to solve this problem, frequency chirp excitation was proposed and evaluated both numerically and experimentally. First, propagation of an HIFU burst through multi-layer media was simulated in a nonlinear acoustic model using the angular spectrum approach. Influences of axial focus shifting on the acoustic intensity at the both grating and main lobes at different excitation frequencies were investigated. It was found that different excitation frequencies result in variations in the position and magnitude of the grating lobe in the pre-focal region, but have little influence on the main lobe. Thus, the frequency chirp excitation can spread the acoustic energy in the pre-focal region, and subsequently reduce the temperature elevation. The performances of downward and upward frequency chirps in different sweeping times were compared to those of conventional excitation at the constant frequency. Then, HIFU plane ablation was evaluated. Even without the cooling time between treatment spots when using the frequency chirps, the pre-focal heating was still less than that at the constant frequency. Finally, the thermocouple measurement in the gel phantom showed an ~40% reduction in pre-focal temperature elevations produced by a single-element concave HIFU transducer using the frequency chirps. Altogether, the frequency chirp excitation could effectively reduce the pre-focal grating lobe at a large axial focus shifting distance, which may enhance both the efficacy and safety of clinical HIFU ablation.

Coupling of Acoustic Cavitation with Dem-Based Particle Solvers for Modeling De-agglomeration of Particle Clusters in Liquid Metals

The aerospace and automotive industries are seeking advanced materials with low weight yet high strength and durability. Aluminum and magnesium-based metal matrix composites with ceramic micro- and nano-reinforcements promise the desirable properties. However, larger surface-area-to-volume ratio in micro- and especially nanoparticles gives rise to van der Waals and adhesion forces that cause the particles to agglomerate in clusters. Such clusters lead to adverse effects on final properties, no longer acting as dislocation anchors but instead becoming defects. Also, agglomeration causes the particle distribution to become uneven, leading to inconsistent properties. To break up clusters, ultrasonic processing may be used via an immersed sonotrode, or alternatively via electromagnetic vibration. This paper combines a fundamental study of acoustic cavitation in liquid aluminum with a study of the interaction forces causing particles to agglomerate, as well as mechanisms of cluster breakup. A non-linear acoustic cavitation model utilizing pressure waves produced by an immersed horn is presented, and then applied to cavitation in liquid aluminum. Physical quantities related to fluid flow and quantities specific to the cavitation solver are passed to a discrete element method particles model. The coupled system is then used for a detailed study of clusters’ breakup by cavitation.