Acoustic Pressure Field Research Articles

On nonlinear effects in holographic-modulated ultrasound

Holographic acoustic lenses (HALs), also known as acoustic holograms, are used for generating unprecedented complex focused ultrasound (FU) fields. HALs store the phase profile of the desired wavefront, which is used to reconstruct the acoustic pressure field when illuminated by a single acoustic source. Nonlinear effects occur as the sound intensity increases, leading to distorted and asymmetric waveforms. Here, the k-space pseudospectral method is used to perform homogeneous three-dimensional nonlinear acoustic simulations with power law absorption. An in-depth analysis is performed to study the evolution of holographic-modulated FU fields produced by HALs as the excitation amplitude increases. It is shown that nonlinear waveform distortion significantly affects the reconstruction of the pressure pattern when compared to the linear condition. Diffraction and nonlinear effects result in an asymmetric waveform with distinct positive and negative pressure patterns at the target plane. Peak positive pressure distribution becomes more localized around the areas with the highest nonlinear distortion. The peak signal-to-distortion ratio (PSDR) at the target plane falls while the nonuniformity index (NUI) rises. As a result of harmonic generation, the heat deposition distribution becomes highly localized with a significant increase in the NUI. Nonlinear effects have also been shown to flatten the peak negative pressure distribution while having minimal effect on the PSDR or NUI. However, nonlinear effects are shown to be critical for accurately predicting cavitation zones. Findings will pave the way for HALs implementation in high-intensity applications and prompt the incorporation of nonlinear acoustics into the notion of computer-generated holography.

Numerical Study of the Impact of Fluid–Structure Interaction on Flow Noise over a Rectangular Cavity

Fluid–structure interactions (FSI) can significantly affect flow and the acoustic field generated by it. In this article, simulations of the flow over a rectangular cavity are conducted with and without taking FSI into account. The aim of this research is to conduct a numerical study of the flow over a cavity and to verify whether interactions between the flow and the elastic structure can significantly affect the flow itself or the acoustic pressure field. Four cases involving flexible walls with different material parameters and one reference case with rigid walls were analysed. The two-directional fluid–structure coupling between the flow and cavity walls was simulated. The simulations were performed with the volume and finite element methods using OpenFOAM software to solve the fluid field, CalculiX software to solve the displacement of the structure, and the preCICE library to couple the codes and computed fields. The acoustic analogy of Ffowcs-Williams and Hawkings and the libAcoustics library were used to calculate the sound pressure. The simulation results showed that FSI has a significant influence on sound pressure in terms of both pressure amplitudes and levels as well as in terms of noise frequency composition. There was a significant increase in the sound pressure compared to the case with rigid walls, especially for frequencies above 1 kHz. The frequencies at which this occurred are related to the natural frequencies of the cavity walls and the Rossiter frequencies. Overlap of these frequencies may lead to an increase in noise and structural vibrations, which was observed for one of the materials used. This study may provide insight into the flow noise generation mechanism when fluid–structure interactions are taken into account. The conclusions presented here can form a basis for further work on aerodynamic noise in the presence of thin-walled structures.

Synthetic Pseudo-Spin-Hall effect in acoustic metamaterials

While vector fields naturally offer additional degrees of freedom for emulating spin, acoustic pressure field is scalar in nature, and it requires engineering of synthetic degrees of freedom by material design. Here we experimentally demonstrate the control of sound waves by using two types of engineered acoustic systems, where synthetic pseudo-spin emerges either as a consequence of the evanescent nature of the field or due to lattice symmetry. First, we show that evanescent sound waves in perforated films possess transverse angular momentum locked to their propagation direction which enables their directional excitation. Second, we demonstrate that lattice symmetries of an acoustic kagome lattice also enable a synthetic transverse pseudo-spin locked to the linear momentum, enabling control of the propagation of modes both in the bulk and along the edges. Our results open a new degree of control of radiation and propagation of acoustic waves thus offering new design approaches for acoustic devices.

A numerical strategy for predicting the coupling-strength of acoustic fluid-structure interaction

The coupling-strength analysis can guide the proper modeling and efficient response analysis for acoustic fluid–structure problems. In this paper, a coupling-strength factor is proposed to quantify the dynamic interaction between acoustic fluid and structure, and its efficient computational strategy is established via a fast algorithm. This dimensionless factor expresses the average difference between the uncoupled and the coupled structural displacement (acoustic pressure) fields. The factor expression is related to the coupling matrix and the dynamic flexibility matrices of each physical field for the discrete system. Then a fast dynamic flexibility matrix algorithm of the non-positive definite system is deduced to ensure the feasibility of numerically calculating the factor, and the effects of the unconstrained structure and the acoustic rigid wall on the coupling-strength can be observed. Additionally, the strongly decoupling eigen-equations of each physical field are derived by the dynamic flexibility matrix expansion. Solving the resonance frequencies is adopted to verify the correctness of the proposed coupling-strength analysis strategy. In numerical examples, the coupling-strength factor is high-efficiently calculated with acceptable accuracy, the coupling-strength is investigated for the various acoustic fluid mediums and different boundary conditions, and the applicability and effectiveness of the factor are verified.

Acoustic levitation of axisymmetric Mie objects above a transducer array by engineering the acoustic radiation force and torque.

Transducer arrays are a versatile tool for the contactless manipulation of spherical Rayleigh objects. Here we propose an analytical model for stable levitation of axisymmetric Mie objects through directly engineering the desired radiation force and torque. Acoustic contributions from multiple transducers are superimposed through the translation addition theorem, and the nonspherical objects are mapped into a sphere using the conformal transformation technique so that the scattered field can be asymptotically obtained. Then we give the acoustic radiation force and torque applied to a rigid nonspherical Mie object, which can be reconstructed as a series of quasiexplicit functions of the transducer (amplitude and phase) parameters. Through specifying the desired radiation force and torque exerted on the objects, a system of nonlinear equationsis produced, which could be iteratively solved to retrieve appropriate transducer parameters that stabilize the object in an equilibrium position. Practically, we demonstrate several examples of stable levitation of a sphere, a spheroid, and a disk with an averaged radius of a=7mm (size parameter of ka≈5.18) above a transducer array. The absolute acoustic pressure field surrounding the objects simulated by the finite-element method is illustrated to verify the trapping results. The developed analytical model provides an alternative approach to retrieve the transducer parameters for levitating macroscopic nonspherical rigid objects, which may help design the systematic dynamical manipulation of Mie particles.

Models for resonant acoustic metasurfaces with application to moth wing ultrasound absorption.

Taking as bioinspiration the remarkable acoustic absorption properties of moth wings, we develop a simple analytical model that describes the interaction between acoustic pressure fields, and thin elastic plates incorporating resonant sub-structures. The moth wing is an exemplar of a natural acoustic metamaterial; the wings are deeply subwavelength in thickness at the frequencies of interest, the absorption is broadband and the tiny scales resonate on the moth wing acting in concert. The simplified model incorporates only the essential physics and the scales are idealized to flat rigid rectangular plates coupled via a spring to an elastic plate that forms the wing; all the components are deep-subwavelength at desired frequencies. Based on Fourier analysis, complemented by phenomenological modelling, our theory shows excellent agreement with simulation mimicking the moth-wing structure. Moth wings operate as broadband sound absorbers employing a range of scale sizes. We demonstrate that a random distribution of scale sizes generates a broadband absorption spectrum. To further illustrate the potential of the model, we design a deeply sub-wavelength acoustic counterpart of electromagnetically induced reflectance.This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’.

Optimal stochastic modeling in random media propagation: Dynamically orthogonal parabolic equations?

Reliable underwater acoustic propagation is challenging due to complex ocean dynamics such as internal-waves and to the uncertain larger-scale ocean physics, acoustics, bathymetry, and seabed fields. For accurate acoustic propagation, capturing the important environmental uncertainties and variabilities and predicting the probability distributions of the acoustic pressure field is then what matters. Prior works towards addressing this goal include (i) wave propagation in random media techniques such as perturbation methods, path integral theory, and coupled-mode transport theory, and (ii) probabilistic modeling techniques such as Monte Carlo sampling and Polynomial Chaos expansions. Recently, we developed a novel technique called the Dynamically Orthogonal Parabolic Equations (DO-ParEq) which represent the sound speed, density, bathymetry, and acoustic pressure fields using optimal dynamic Karhunen-Loeve decompositions. The DO-ParEq are range-evolving partial and stochastic differential equations preserving acoustic nonlinearities and non-Gaussian properties. In this presentation, we showcase the theoretical and computational advantages of the DO-ParEq framework compared to the state-of-the-art techniques in the Pekeris waveguide and wedge benchmark problems, in addition to a realistic ocean example in the New York Bight region.

Lattice Boltzmann very large eddy simulations of a turbulent flow over covered and uncovered cavities

Microphone measurements in a closed test section wind tunnel are affected by turbulent boundary layer (TBL) pressure fluctuations. These fluctuations are mitigated by placing the microphones at the bottom of cavities, usually covered with a thin, acoustically transparent material. Prior experiments showed that the cavity geometry affects the propagation of TBL pressure fluctuations toward the bottom. However, the relationship between the cavity geometry and the flowfield within the cavity is not well understood. Therefore, a very large-eddy simulation was performed using the lattice Boltzmann method. A cylindrical, a countersunk and a conical cavity are simulated with and without a fine wire-cloth cover, which is modeled as a porous medium governed by Darcy's law. Adding a countersink to an uncovered cylindrical cavity is found to mitigate the transport of turbulent structures across the bottom by shifting the recirculation pattern away from the cavity bottom. Covering the cavities nearly eliminates this source of hydrodynamic pressure fluctuations. The eddies within the boundary layer, which convect over the cover, generate a primarily acoustic pressure field inside the cavities and thus suggesting that the pressure fluctuations within covered cavities can be modeled acoustically. As the cavity diameter increases compared to the eddies' integral length scale, the amount of energy in the cut-off modes increases with respect to the cut-on modes. Since cut-off modes decay as they propagate into the cavity, more attenuation is seen. The results are in agreement with experimental evidence.

Microphone vibration sensitivity: What it is, why it is important, and how to measure it

Microphones are designed to respond to acoustic pressure fields, but they can also be excited by external sources of mechanical vibration. In hearing aids, feedback is a difficult problem to resolve due to the high gain used to amplify sounds. The problem is worsened by the location of microphones and loudspeakers in close proximity, coupling both the acoustic and mechanical feedback paths. The first proposals of microphone vibration measurement techniques and definitional structure were published by Mead Killion in the 1970’s. Significant improvements in measurement technique have been published over the last 10 years. This talk will focus on a new measurement technique that allows for direct measurement of the “intrinsic vibration sensitivity”. The technique gives the ideal zero acoustic pressure condition at the microphone port and isolates room acoustic noise from the desired vibration signal. The noise floor of the new technique is 30 dB below previous methods, allowing for exceptionally clean measurement of primary-axis vibration sensitivity up to 10 kHz. Improvements are robust enough to enable the clean measurement of off-axis sensitivity of the microphone, which is often below 50 dBspl equivalent at 9.81 m/s2 of acceleration.

Temperature as a key parameter for graphene sono-exfoliation in water

Graphene dispersions in water are highly desirable for a range of applications such as biomedicines, separation membranes, coatings, inkjet printing and more. Recent novel research has been focussed on developing a green approach for scalable production of graphene. However, one important parameter, which is often neglected is the bulk temperature of the processing liquid. This paper follows our earlier work where optimal sono-exfoliation parameters of graphite in aqueous solutions were determined based on the measured acoustic pressure fields at various temperatures and input powers. Here, we take the next step forward and demonstrate using systematic characterisation techniques and acoustic pressure measurements that sonication-assisted liquid phase exfoliation (LPE) of graphite powder can indeed produce high quality few layer graphene flakes in pure water at a specific temperature, i.e. 40 °C, and at an optimised input generator power of 50%, within 2-h of processing. UV–vis analysis also revealed that the exfoliation, stability and uniformity of dispersions were improved with increasing temperature. We further confirmed the successful exfoliation of graphene sheets with minimal level of defects in the optimized sample with the help of Raman microscopy and transmission electron microscopy. This study demonstrated that understanding and controlling processing temperature is one of the key parameters for graphene exfoliation in water which offers a potential pathway for its large-scale production.

Modeling of an Impedimetric Biosensor with Ultrasonic-Assisted Cell Alignment for the Detection of Yeast

Yeast is an integral part of our environment. The detection of yeast is of great significance in many fields. The impedance-based sensor with interdigital microelectrodes is a promising method to establish a simple and portable detection system. However, the positions of yeast cells greatly influence the impedance variation and eventually the sensitivity of detection. In this study, an impedimetric biosensor with ultrasonic-assisted cell alignment for yeast detection was proposed. In order to verify the feasibility of this biosensor, finite element modeling was conducted using the software COMSOL. The acoustic pressure field and the acoustic radiation force exerted on yeast cells were investigated. Cell positions in the microfluidic channel were determined using the fluid particle tracking module. After that, the impedance between the microelectrodes was calculated. Yeast suspensions with different cell concentrations were used as the tested samples for the simulation. The proposed sensor showed a higher sensitivity than the conventional impedimetric biosensor on which the cells were randomly located. It can be used for the detection of microorganisms. This finite element modeling provided an effective approach for the design of biosensors.

Acoustic Resonance Frequencies of Underwater Toroidal Bubbles.

Underwater bubbles display an acoustic resonance frequency close to spherical ones. In order to obtain a resonance significantly deviating from the spherical case, we stabilize bubbles in toroidal frames, resulting in bubbles which can be slender while still compact. For thin tori the resonance frequency increases greatly. Between a pair of bubble rings, we can achieve a flat acoustic pressure field for a critical distance between rings, a condition reminiscent of Helmholtz coils in magnetostatics. This opens the possibility to shape the acoustic field using long tunnels of rings.

Experimental Validations of Reconstructed Excitation Forces Acting Inside a Solid Enclosure. Part I: Exterior Region

This paper presents the experimental validations of reconstructing the characteristics of the excitation forces that act inside a vibrating structure, which includes the location, type, amplitude, and spectrum, based on a single set of measurements of the normal surface velocity on the exterior surface by using the modified Helmholtz Equation Least Squares (HELS) method, as if one could see through this solid structure. Phase I of this paper shows the reconstruction of the vibroacoustic responses in the exterior region of the structure, including the field acoustic pressure, the surface acoustic pressure, the normal surface velocity or Operational Deflection Shape (ODS), the normal component of the time-averaged acoustic intensity, and the time-averaged acoustic power. Phase II of this paper illustrates the reconstruction of the excitation forces with the fluid-loading effects taken into consideration, based on the vibroacoustic responses reconstructed in the exterior region. The significance of the study, namely, the interrelationships among the excitation force, structural vibration, and acoustic radiation is discussed. The knowledge thus acquired may be important for engineers to analyze various complex noise and vibration issues in practice and to come up with the most cost-effective noise and vibration mitigation strategies.

Hydraulic optimization design of centrifugal pumps aiming at low vibration noise

In order to reduce the vibration noise generated by the centrifugal pump in the working process and improve the working efficiency of the centrifugal pump, the sound field numerical calculation of IS80-65-160 single-stage single-suction centrifugal pump was carried out. Under the condition that the parameters of the pump body and the impeller remain unchanged, the number of blades of the prototype pump impeller was designed as 4, 5, 6, and 7, respectively. The flow-induced vibration and noise characteristics of centrifugal pumps were studied from two aspects of numerical simulation and test, and the renormalization group k-ε model was used to simulate the steady and unsteady state of centrifugal pumps with different blade numbers. The external characteristics, pressure pulsation characteristics, vibration, and noise of the centrifugal pump were obtained, and the flow-induced vibration and noise test platform of the centrifugal pump was built for experimental verification. The research showed that the flow induction in the model pump was the main factor affecting the vibration of the prototype pump, and the shaft frequency and blade frequency were the main reasons causing the noise of the prototype pump. The vibration of each blade was the most concentrated at onefold blade frequency, and the peak of the sound field acoustic pressure level of the pump body was higher than other frequencies at threefold blade frequency, which was most obvious in the tongue region of the volute. With the increase of blades, the noise in volute decreased. The vibration intensity of the 4-blade prototype pump was lower, but the efficiency and head were also lower. The vibration intensity of the 5-blade prototype pump was the highest, the comprehensive performance of the 6-blade prototype pump was better, and the vibration of the 7-blade prototype pump was unstable. The test results showed that six blades could effectively reduce the flow-induced vibration noise of centrifugal pumps and improve the working environment, which provided certain application value and guiding significance for the hydraulic design of the subsequent low-noise centrifugal pumps.

High-Frequency Self-Focusing Ultrasonic Transducer With Piezoelectric Metamaterial

Focused ultrasonic waves are widely used in medical imaging, fibroids ablation and acoustic tweezers due to its high sensitivity and large energy at the focal spot. Although, acoustic metamaterials have emerged for acoustic focusing, they have limited to low frequency, narrowband and less acoustic transmission. Herein, an active gradient metamaterial (AGM) based on composite structure on traditional piezoelectric materials is proposed to achieve the acoustic impedance matching and underwater acoustic focusing. Based on the principle that the acoustic wave emitted from the piezoelectric plate reaches the focal spot at the same time, an aperiodic axisymmetric composite with gradient depth is established. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$200 ~\mu \text{m}$ </tex-math></inline-formula> kerf is selected, and the depth ranges from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$44 ~\mu \text{m}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$146 ~\mu \text{m}$ </tex-math></inline-formula> . The acoustic field pressure intensity is simulated with finite element software, and measured by a needle hydrophone with fabricated transducer. Based on the good agreement between the simulation and experimental results with the excitation frequency range of 4 MHz-20 MHz, the active self-focusing and broadband focusing behaviors of the AGM are demonstrated. It is expected to apply the proposed acoustic metamaterial in biomedical and industrial applications.

Study on bandgap of a novel phononic crystal with low-frequency sound insulation

To solve the problem of low-frequency noise in the environment, a two-dimensional Helmholtz-type phononic crystal with a labyrinth tube was designed in the paper. First, the low-frequency band structure was calculated by the finite element method (FEM) and transfer matrix method (TMM). Second, the bandgap formation was analyzed by using an acoustic pressure field, and the “spring-oscillator” equivalent model of the structure was established. Finally, the influences of structural parameters on the first bandgap were investigated. Results show that there are four bandgaps in the frequency range of 0–300 Hz, and the lower limit of the first bandgap can be as low as 12.15 Hz, which improves the low-frequency sound insulation ability of phononic crystals of the same size. The calculation results of the two methods (FEM and TMM) are basically consistent. Research on the influencing factors of the bandgap shows that the increase in the length of the tube will reduce the upper and lower limits of the bandgap and narrow the bandgap width. With the increase of the lattice constant, the upper limit of the bandgap decreases, while the lower limit of the bandgap remains unchanged. The design provides a new method to solve the problem of low-frequency noise reduction.

Acoustophoresis in suspensions with local and time-discrete sound fields based on the time reversal technique

Abstract. In this paper, a new approach of three-dimensional acoustic particle manipulation (acoustophoresis) in closed and liquid-filled vessels based on the time reversal technique is discussed. Based on simulation studies, this work investigates the technical prerequisites to achieve appropriate acoustic radiation forces (ARFs) for the manipulation of small particles with the time reversal method by utilizing multiple reflections in a closed vessel. The time-discrete and localized acoustic pressure field required for this purpose is generated by a time reversal mirror composed of 24 piezoceramic transducers. The paper also gives an outlook on practical evaluation of the simulation results based on a demonstrator setup.

Topology optimization for acoustic structures considering viscous and thermal boundary layers using a sequential linearized Navier–Stokes model

This study proposes a level set-based topology optimization method for designing acoustic structures with viscous and thermal boundary layers in perspective. Acoustic waves propagating in a narrow channel are damped by viscous and thermal boundary layers. To estimate these viscothermal effects, we first introduce a sequential linearized Navier–Stokes model based on three weakly coupled Helmholtz equations for viscous, thermal, and acoustic pressure fields. Then, the optimization problem is formulated, where a sound-absorbing structure comprising air and an isothermal rigid medium is targeted, and its sound absorption coefficient is set as an objective function. The adjoint variable method and the concept of the topological derivative are used to approximately obtain design sensitivity. A level set-based topology optimization method is used to solve the optimization problem. Two-dimensional numerical examples are provided to support the validity of the proposed method. Moreover, the mechanisms that lead to the high absorption coefficient of the optimized design are discussed.

Differential evolution method to find optimal location of a single-element transducer for transcranial focused ultrasound therapy

Background and objectiveFocused ultrasound (FUS) has been receiving growing attention as a noninvasive brain stimulation tool because of its superior spatial specificity and depth penetrability. However, the large mismatch of acoustic properties between the skull and water can disrupt and shift the acoustic focus in the brain. In this paper, we present a numerical method to find the optimal location of a single-element FUS transducer, which creates focus on the target region. MethodsThe score function, representing the superposition of acoustic waves according to the relative phase difference and transmissibility, was defined based on time-reversal invariance of acoustic waves and depending on the spatial location of the transducer. The optimal location of the transducer was then determined using a differential evolution algorithm. To assess the proposed method, we conducted a forward simulation and compared the resulting focal location to the desired target point. We also performed experimental validation by measuring the acoustic pressure field through an ex vivo human skull in a water tank. ResultsThe numerical results indicated that the score function had a positive proportional relationship with the acoustic pressure at the target. Moreover, for the optimized transducer location, both the numerical and experimental results showed that the normalized acoustic pressure at the target was higher than 0.9. ConclusionsIn this study, we developed an optimization method to place a single-element transducer that effectively transmits acoustic energy to the targeted region in the brain. Our numerical and experimental results demonstrate that the proposed method can provide an optimal transducer location for safe and efficient FUS treatment.

Finite element hybrid and direct computational aeroacoustics at low Mach numbers in slow time-dependent domains

In this work, we address the finite element computation of flow noise in the presence of arbitrarily slowly moving rigid bodies at low Mach numbers, by means of hybrid and direct computational aeroacoustics (CAA) strategies. As regards the former, the problem could be dealt with by means of the Ffowcs Williams–Hawkings acoustic analogy. That reduces to Curle’s analogy for a static body, which is analogous to a problem of diffraction of sound waves generated by flow eddies in the vicinity of the body. Acoustic analogies in CAA first demand computing the flow motion to extract an acoustic source term from it and then use the latter to calculate the acoustic pressure field. However, in the case of low Mach number flows, the Ffowcs Williams–Hawkings and Curle analogies present a problem as they require knowing the total pressure distribution on the body’s boundary (i.e. the aerodynamic pressure plus the acoustic one). As incompressible computational fluid dynamics (CFD) simulations are usually performed to determine the flow motion, the acoustic pressure distribution on the body surface is unavoidably missing, which can yield acoustic analogies inaccurate. In a recent work, it was proposed to tackle that problem for static and rigid surfaces, by keeping the incompressible CFD and then splitting the acoustic pressure into direct and diffracted components. Two separate wave equations were solved for them, in the framework of the finite element method (FEM). In this article, we extend that work to compute the aerodynamic sound generated by a flow interacting with a slowly moving rigid body. The incompressible Navier–Stokes equations are first solved in an arbitrary Lagrangian–Eulerian (ALE) frame of reference to obtain the acoustic source term. Advantage is then taken from the same computational run to separately solve two acoustic ALE wave equations in mixed form for the incident and diffracted acoustic pressure components. For validation of the total acoustic pressure field, an ALE formulation of a direct CAA approach consisting of a unified solver for a compressible isentropic flow in primitive variables is considered. The performance of the exposed methods is illustrated for the aeroacoustics of flow past a slowly oscillating two-dimensional NACA airfoil and for flow exiting a duct with a moving teeth-shaped obstacle at its termination.