Acoustic waves in two-fraction mixtures of liquid with vapor-gas bubbles

2012 ◽  
Vol 9 (1) ◽  
pp. 65-68
Author(s):  
R.N. Gafiyatov
Keyword(s):  
Acoustic Waves ◽  
Gas Bubbles ◽  
Transformation Method ◽  
Fast Fourier Transformation ◽  
Fourier Transformation Method ◽  
Impulse Pressure ◽  
Pressure Perturbations ◽  
The Mathematical Model ◽  
Different Gases ◽  
Fractional Mixture

The mathematical model of two-fractional mixture of liquid with vapor-gas bubbles of different gases and sizes with phase transformations is presented. The dispersive equation is received, dispersive curves that determine the propagation of acoustic disturbances was plotted. Calculations on the propagation of impulse pressure perturbations were performed by means of a fast Fourier transformation method.

scholarly journals Fast Fourier Transformation method for computing the permeability of periodic porous media

2017 ◽  
Vol 39 (2) ◽  
pp. 121-133
Author(s):  
Nguyen Trung Kien ◽  
Nguyen Duy Hung
Keyword(s):  
Porous Media ◽  
Fourier Transformation ◽  
Linear Problem ◽  
Stokes Equations ◽  
Solid Phase ◽  
Transformation Method ◽  
Fast Fourier Transformation ◽  
Fourier Space ◽  
Fourier Transformation Method ◽  
Rigid Skeleton

A Fourier-based method is adopted to determine the permeability of periodic porous media made up of a rigid skeleton saturated by viscous fluid. The flow, induced by a prescribed macroscopic gradient of pressure, adopts the Stokes equations with incorporating a condition of adherence at the surface of the solid. The permeability is determined by solving a linear problem on a unit cell for which we determine the local velocity fields due to a prescribed gradient of pressure. The method uses the Fourier Transformation and exact expressions of the periodic Green tensor in the Fourier space. It is shown that the resolution of the problem requires an introducing of undetermined forces acting within the solid phase.

scholarly journals FFT simulations and multi-coated inclusion model for macroscopic conductivity of 2D suspensions of compound inclusions

2015 ◽  
Vol 37 (3) ◽  
pp. 169-176
Author(s):  
Nguyen Van Luat ◽  
Nguyen Trung Kien
Keyword(s):  
Approximation Method ◽  
Fourier Transformation ◽  
Dimensional Space ◽  
Transformation Method ◽  
Fast Fourier Transformation ◽  
Two Dimensional ◽  
Random Models ◽  
Coated Inclusion ◽  
Fourier Transformation Method ◽  
Fast Fourier Transformation Method

Article introduces the Fast-Fourier transformation method (FFT) and an approximation method to calculate the conductivity of compound-inclusion composites in two-dimensional space. The approximation compares favorably with the numerical results for a number of periodic and random models over a range of volume proportions of phases, but divers at large volume proportions of the included phases when the interactions between the inclusions are more pronounced.

scholarly journals Potential of Workshop Measurement Positioning System to Measure Oscillation Frequencies of Rigid Structures

2019 ◽  
Vol 9 (3) ◽  
pp. 595 ◽  
Author(s):  
Chunbao Xiong ◽  
Hongzhi Bai ◽  
Jiarui Lin
Keyword(s):  
Three Dimensional ◽  
Transformation Method ◽  
Fast Fourier Transformation ◽  
Positioning System ◽  
Test Bed ◽  
Coordinate Measurement ◽  
Intrinsic Parameters ◽  
High Measurement ◽  
Fourier Transformation Method ◽  
Oscillation Frequencies

A workshop measuring and positioning system (wMPS) is a large three-dimensional (3D) coordinate-measurement system based on optoelectronic scanning. It is capable of large-range coverage, high measurement accuracy and frequency, and multi-task synchronous measurement. Existing geodetic instruments cannot measure the intrinsic parameters of strong rigid structures. Thus, this study conducted experiments to explore the feasibility of the wMPS to measure the intrinsic parameters of rigid structures. A test bed was established using a reverse-engineering method to simulate the oscillation frequency of the structure. Displacement data, which changed with the time series through the fast Fourier transformation method, were analyzed to determine the feasibility and range of the wMPS in measuring intrinsic parameters of the structure. The experimental results demonstrated that the wMPS can measure the vibrational frequency up to 9 Hz with a 3-mm amplitude and up to 4 Hz with a 30-mm amplitude.

scholarly journals A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous Oscillators

1995 ◽  
Vol 2 (3) ◽  
pp. 205-218 ◽  
Author(s):  
T. Ge ◽  
A. Y. T. Leung
Keyword(s):  
Harmonic Balance ◽  
Fourier Transformation ◽  
Harmonic Balance Method ◽  
Numerical Differentiation ◽  
Transformation Method ◽  
Fast Fourier Transformation ◽  
Arc Length ◽  
Nonlinear Characteristics ◽  
Fourier Transformation Method ◽  
Branch Switching

A semianalytical algorithm is proposed for the solutions and their stability of a piecewise nonlinear system. The conventional harmonic balance method is modified by the introduction of Toeplitz Jacobian matrices (TJM) and by the alternative applications of fast Fourier transformation (FFT) and its inverse. The TJM/FFT method substantially reduces the amount of computation and circumvents the necessary numerical differentiation for the Jacobian. An arc-length algorithm and a branch switching procedure are incorporated so that the secondary branches can be independently traced. Oscillators with piecewise nonlinear characteristics are taken as illustrative examples. Flip, fold, and Hopf bifurcations are of interest.

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 Two-phase flow equations for a dilute dispersion of gas bubbles in liquid

1984 ◽  
Vol 148 ◽  
pp. 301-318 ◽  
Author(s):  
A. Biesheuvel ◽  
L. Van Wijngaarden
Keyword(s):  
Acoustic Waves ◽  
Equations Of Motion ◽  
Gas Bubbles ◽  
Local Stress ◽  
Mass Conservation ◽  
Ensemble Averaging ◽  
Two Phase ◽  
Average Force ◽  
Gas Concentration ◽  
Flow Equations

Equations of motion correct to the first order of the gas concentration by volume are derived for a dispersion of gas bubbles in liquid through systematic averaging of the equations on the microlevel. First, by ensemble averaging, an expression for the average stress tensor is obtained, which is non-isotropic although the local stress tensors in the constituent phases are isotropic (viscosity is neglected). Next, by applying the same technique, the momentum-flux tensor of the entire mixture is obtained. An equation expressing the fact that the average force on a massless bubble is zero leads to a third relation. Complemented with mass-conservation equations for liquid and gas, these equations appear to constitute a completely hyperbolic system, unlike the systems with complex characteristics found previously. The characteristic speeds are calculated and shown to be related to the propagation speeds of acoustic waves and concentration waves.

A Generalized Equation for Scattering Cross Section of Spherical Gas Bubbles Oscillating in Liquids Under Acoustic Excitation

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Yuning Zhang
Keyword(s):  
Cross Section ◽  
Acoustic Waves ◽  
Ambient Pressure ◽  
Gas Bubbles ◽  
Resonance Region ◽  
Generalized Equation ◽  
Scattering Cross Section ◽  
Acoustic Excitation ◽  
Spherical Waves ◽  
Scattering Cross

When irradiated by acoustic waves, gas bubbles can generate divergent spherical waves, which are frequently used to detect the sizes and number density of the gas bubbles. In this paper, a generalized equation for scattering cross section of spherical gas bubbles oscillating in liquids under acoustic excitation is proposed. Comparing with formulas in the literature, this generalized equation can improve the predictions of acoustical scattering cross section in the near-resonance region with high ambient pressure and above-resonance region.

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