Theoretical Studies of Nonlinear Generation Efficiency in a Bubble Layer

2012 ◽  
Vol 37 (3) ◽  
pp. 287-294 ◽  
Author(s):  
Anna Baranowska
Keyword(s):  
Acoustic Waves ◽  
Volume Fraction ◽  
Second Harmonic ◽  
Environmental Parameters ◽  
Bubbly Liquid ◽  
Reflected Waves ◽  
Spherical Bubbles ◽  
Bubble Layer ◽  
The Mathematical Model ◽  
Dissipative Wave Equation

Abstract The aim of the paper is a theoretical analysis of propagation of high-intensity acoustic waves throughout a bubble layer. A simple model in the form of a layer with uniformly distributed mono-size spherical bubbles is considered. The mathematical model of the pressure wave’s propagation in a bubbly liquid layer is constructed using the linear non-dissipative wave equation and assuming that oscillations of a single bubble satisfy the Rayleigh-Plesset equation. The models of the phase sound speed, changes of resonant frequency of bubbles and damping coefficients in a bubbly liquid are compared and discussed. The relations between transmitted and reflected waves and their second harmonic amplitudes are analyzed. A numerical analysis is carried out for different environmental parameters such as layer thicknesses and values of the volume fraction as well as for different parameters of generated signals. Examples of results of the numerical modeling are presented.

scholarly journals Reflection and Transmission of Acoustic Waves through the Layer of Multifractional Bubbly Liquid

2018 ◽  
Vol 148 ◽  
pp. 15001
Author(s):  
Damir Anvarovich Gubaidullin ◽  
Ramil Nakipovich Gafiyatov
Keyword(s):  
Acoustic Waves ◽  
Wave Reflection ◽  
Water Model ◽  
Bubbly Liquid ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Multilayer Medium ◽  
Bubble Layer ◽  
The Mathematical Model ◽  
Theoretical Results

The mathematical model that determines reflection and transmission of acoustic wave through a medium containing multifractioanl bubbly liquid is presented. For the water-water with bubbles-water model the wave reflection and transmission coefficients are calculated. The influence of the bubble layer thickness on the investigated coefficients is shown. The theory compared with the experiment. It is shown that the theoretical results describe and explain well the available experimental data. It is revealed that the special dispersion and dissipative properties of the layer of bubbly liquid can significantly influence on the reflection and transmission of acoustic waves in multilayer medium

scholarly journals Experimental demonstration of negative refraction with 3D locally resonant acoustic metafluids

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Benoit Tallon ◽  
Artem Kovalenko ◽  
Olivier Poncelet ◽  
Christophe Aristégui ◽  
Olivier Mondain-Monval ◽  
...  
Keyword(s):  
Experimental Data ◽  
Yield Stress ◽  
Multiple Scattering ◽  
Silicone Rubber ◽  
Acoustic Waves ◽  
Scattering Theory ◽  
Negative Refraction ◽  
Volume Fraction ◽  
Experimental Demonstration ◽  
Acoustic Beam

AbstractNegative refraction of acoustic waves is demonstrated through underwater experiments conducted at ultrasonic frequencies on a 3D locally resonant acoustic metafluid made of soft porous silicone-rubber micro-beads suspended in a yield-stress fluid. By measuring the refracted angle of the acoustic beam transmitted through this metafluid shaped as a prism, we determine the acoustic index to water according to Snell’s law. These experimental data are then compared with an excellent agreement to calculations performed in the framework of Multiple Scattering Theory showing that the emergence of negative refraction depends on the volume fraction $$\Phi$$ Φ of the resonant micro-beads. For diluted metafluid ($$\Phi =3\%$$ Φ = 3 % ), only positive refraction occurs whereas negative refraction is demonstrated over a broad frequency band with concentrated metafluid ($$\Phi =17\%$$ Φ = 17 % ).

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

A PHASE-PLANE DESCRIPTION OF NONLINEAR TRAVELING WAVES IN BUBBLY LIQUIDS

1999 ◽  
Vol 07 (02) ◽  
pp. 71-82
Author(s):  
A. NADIM ◽  
D. GOLDMAN ◽  
J. J. CARTMELL ◽  
P. E. BARBONE
Keyword(s):  
Equation Of State ◽  
Fixed Points ◽  
Traveling Wave ◽  
Phase Plane ◽  
Volume Fraction ◽  
Low Frequency ◽  
Traveling Wave Solutions ◽  
Bubbly Liquid ◽  
Phase Plane Analysis ◽  
Bubbly Liquids

One-dimensional traveling wave solutions to the fully nonlinear continuity and Euler equations in a bubbly liquid are considered. The elimination of velocity from the two equations leaves a single nonlinear algebraic relation between the pressure and density profiles in the mixture. On assuming the bubbles to have identical size and taking the volume fraction of bubbles in the medium to be small, an equation of state which relates the mixture pressure to the density and its first two material time-derivatives is derived. When this equation of state is linearized and combined with the laws of conservation of mass and momentum, a nonlinear, second-order, ordinary differential equation is obtained for the density as a function of the single traveling wave coordinate. A phase-plane analysis of this equation reveals the existence of two fixed points, one of which is a saddle and the other a node. A single trajectory connects the two fixed points and corresponds to a traveling shock wave solution when the Mach number of the wave, defined as the ratio of traveling wave speed to the low-frequency speed of sound in the bubbly liquid, exceeds unity. The analysis provides a qualitative explanation of the oscillations behind shocks seen in experiments on bubbly liquids.

A three-microphone acoustic reflection technique using transmitted acoustic waves in the airway

2013 ◽  
Vol 115 (8) ◽  
pp. 1119-1125 ◽  
Author(s):  
Yuki Fujimoto ◽  
Jyongsu Huang ◽  
Toshiharu Fukunaga ◽  
Ryo Kato ◽  
Mari Higashino ◽  
...  
Keyword(s):  
Acoustic Waves ◽  
Cross Sectional Area ◽  
Distance Functions ◽  
Sectional Area ◽  
Wave Tube ◽  
Cross Sectional ◽  
Reflected Waves ◽  
Acoustic Reflection ◽  
Obstructive Sleep ◽  
And Function

The acoustic reflection technique noninvasively measures airway cross-sectional area vs. distance functions and uses a wave tube with a constant cross-sectional area to separate incidental and reflected waves introduced into the mouth or nostril. The accuracy of estimated cross-sectional areas gets worse in the deeper distances due to the nature of marching algorithms, i.e., errors of the estimated areas in the closer distances accumulate to those in the further distances. Here we present a new technique of acoustic reflection from measuring transmitted acoustic waves in the airway with three microphones and without employing a wave tube. Using miniaturized microphones mounted on a catheter, we estimated reflection coefficients among the microphones and separated incidental and reflected waves. A model study showed that the estimated cross-sectional area vs. distance function was coincident with the conventional two-microphone method, and it did not change with altered cross-sectional areas at the microphone position, although the estimated cross-sectional areas are relative values to that at the microphone position. The pharyngeal cross-sectional areas including retropalatal and retroglossal regions and the closing site during sleep was visualized in patients with obstructive sleep apnea. The method can be applicable to larger or smaller bronchi to evaluate the airspace and function in these localized airways.

Acoustic Waves Forced in Flowing Bubbly Liquid

1986 ◽  
Vol 55 (2) ◽  
pp. 512-520 ◽  
Author(s):  
Toshinori Toma ◽  
Shigeki Morioka
Keyword(s):  
Acoustic Waves ◽  
Bubbly Liquid

scholarly journals Numerical Study of Hydrodynamic Impact on Bubbly Water

2015 ◽  
Author(s):  
Mehdi Elhimer ◽  
Aboulghit El Malki Alaoui ◽  
Kilian Croci ◽  
Céline Gabillet ◽  
Nicolas Jacques
Keyword(s):  
Volume Fraction ◽  
Numerical Study ◽  
Numerical Data ◽  
Void Volume Fraction ◽  
Bubbly Liquid ◽  
Impact Loads ◽  
Hydrodynamic Impact ◽  
Physical Mechanisms ◽  
The Impact ◽  
The Relationship

The phenomenon of slamming on a bubbly liquid has many occurrences in marine and costal engineering. However, experimental or numerical data on the effect of the presence of gas bubbles within the liquid on the impact loads are scarce and the related physical mechanisms are poorly understood. The aim of the present paper is to study numerically the relationship between the void volume fraction and the impact loads. For that purpose, numerical simulations of the impact of a cone on bubbly water have been performed using the finite element code ABAQUS/Explicit. The present results show the diminution of the impact loads with the increase of the void fraction. This effect appears to be related to the high compressibility of the liquid-gas mixture.

Wavy Motion of Viscous Bubbly Liquid in Tubes of Orthotropic Material

2012 ◽  
Vol 2 (1) ◽  
pp. 39-47
Author(s):  
Rafael Yusif Amenzadeh ◽  
Akperli Reyhan Sayyad ◽  
Faig Bakhman Ogli Naghiyev
Keyword(s):  
Orthotropic Material ◽  
Volume Fraction ◽  
Linear Equations ◽  
Bubbly Liquid ◽  
Air Bubbles ◽  
Two Phase ◽  
One Dimensional ◽  
Wave Characteristics ◽  
Infinite Tube ◽  
Limited Process

This article investigates the pulsating flow of a compressible two-phase bubble of viscous fluid contained in an elastic orthotropicle direct axis tube. In this work, one-dimensional linear equations have been used. It is assumed that the tube is rigidly attached to the certain environment. In the case of finite length the pressure is applied at the end of its faces. In the limited process, relations obtained for a very long tube. Such a description, in a sense generalizes and strengthens the work of this type. In the numerical experiment a semi-infinite tube with flowing water containing small amount of air bubbles is considered. The influence of volume fraction of bubbles on wave characteristics is determined.

scholarly journals On the Diagnosis of Unidirectional Acoustic Waves as Applied to the Measurement of Atmospheric Parameters by the API Method in the SURA Experiment

Atmosphere ◽  
2020 ◽  
Vol 11 (9) ◽  
pp. 924
Author(s):  
Sergey Leble ◽  
Sergey Vereshchagin ◽  
Nataliya V. Bakhmetieva ◽  
Gennadiy I. Grigoriev
Keyword(s):  
Acoustic Waves ◽  
Wave Theory ◽  
Resonant Scattering ◽  
Projection Operators ◽  
Evolution System ◽  
Neutral Atmosphere ◽  
Radio Waves ◽  
Reflected Waves ◽  
Density Perturbations ◽  
Wave Identification

The problem of wave identification is formulated as applied to the results of measurements of the temperature and the density of the neutral atmosphere in the range height 90–120 km by the artificial periodic irregularities (APIs) technique. The technique is based on the resonant scattering of radio waves by artificial periodic irregularities of the ionospheric plasma emerging in the field of a standing wave arising from the interference of the incident and reflected waves from the ionosphere. APIs were created using SURA heating facility (named as SURA experiment). The acoustic wave theory is reformulated on the base of data which can be observed in the given experimental setup. The basic system of equations is reduced so that it accounts only upward and downward directed waves, ignoring entropy mode. The algorithm of wave identification based on usage of dynamic projection operators for such a reduced case is proposed and explicit form of projection operators is derived. Its application to finite number dataset via Discrete Fourier Transform (DFT) is described and results of its application to the DFT-transformed set of experimental observation of the temperature and density perturbations are presented. The result yields hybrid amplitudes, that allow us to calculate energy of the directed waves that enter the observed superposition. The problem of entropy mode detection is discussed, the corresponding projecting operators for the full evolution system are built and a way to apply the method to quantification of it is proposed.

Influence of Relaxation Frequency on Acoustic Wave in Unconsolidated Sands and Acoustic Logging Simulation

2018 ◽  
Vol 26 (02) ◽  
pp. 1850014
Author(s):  
Chongwang Yue ◽  
Xiaopeng Yue
Keyword(s):  
Acoustic Field ◽  
Acoustic Waves ◽  
Relaxation Frequency ◽  
S Wave ◽  
Field Equations ◽  
Acoustic Logging ◽  
Reflected Waves ◽  
Unconsolidated Sands ◽  
Bulk Relaxation ◽  
Shear Relaxation

Apart from consolidated rocks, the effect of relaxation on acoustic propagation in unconsolidated sands cannot be neglected. In this paper, we study the influence of relaxation frequency on the propagation of acoustic waves. We compute the frequency-dependent velocities and attenuation of P1-wave, P2-wave, and S-wave at different bulk or shear relaxation frequency for plane wave. In addition, we derive the integral solutions of acoustic field equations in cylindrical coordinate system to simulate acoustic logging. The reflected acoustic waveforms in a borehole are calculated at different bulk or shear relaxation frequency. Calculation results show that the increase of bulk relaxation frequency will cause the velocity of P1-wave to decrease slightly, and the velocity of P2-wave to decrease substantially. The change of bulk relaxation frequency has no effect on the velocity of S-wave. The increase of bulk relaxation frequency will cause the attenuation of P1-wave or P2-wave to decrease or increase in different wave frequency range. The change of bulk relaxation frequency has no effect on the attenuation of S-wave. The increase of shear relaxation frequency will cause the velocity of P1-wave to increase slightly, and the velocity of P2-wave or S-wave to decrease substantially. The increase of the shear relaxation frequency will cause the attenuation of P1-wave, P2-wave or S-wave to decrease. For acoustic field in a borehole surrounded by unconsolidated sands, the effect of bulk or shear relaxation frequency on the velocity of reflected waves in a borehole is negligible at the dimension of the distance from a logging source. The increase of bulk or shear relaxation frequency will cause the amplitude of the reflected waveforms from the borehole wall to increase.

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