Weakly Nonlinear and High Speed Propagation of Quasi-Monochromatic High Frequency Waves in Compressible Bubbly Liquids

2019 ◽  
Author(s):  
Takanori Yoshimoto ◽  
Tetsuya Kanagawa
Keyword(s):  
High Speed ◽  
Bubble Dynamics ◽  
Multiple Scales ◽  
Compressible Liquid ◽  
Governing Equations ◽  
Nls Equation ◽  
Weakly Nonlinear ◽  
Bubbly Liquids ◽  
High Frequency Waves ◽  
Correction Terms

Abstract This study theoretically investigates plane progressive quasi-monochromatic waves in an initially quiescent compressible liquid containing many spherical gas bubbles, on the basis of the derivation of a nonlinear wave equation that represents waves propagating at a high phase velocity induced by taking the effect of liquid compressibility in consideration. The governing equations for bubbly flows are composed of the conservation equations of mass and momentum, the equation of bubble dynamics as radial oscillations, and so on. By using the method of multiple scales with an appropriate choice of set of scaling relations of nondimensional parameters, the nonlinear Schrödinger (NLS) equation with an attenuation term and some correction terms can be derived from the governing equations. The decrease in the group velocity in a far field is then clarified. The dependence of waveform on wavenumber is implied.

Derivation of an Amplitude Equation for Weakly Nonlinear Pressure Waves of a Very High Frequency in a Compressible Liquid Containing Many Microbubbles

2019 ◽  
Author(s):  
Ryosuke Akutsu ◽  
Tetsuya Kanagawa ◽  
Yusuke Uchiyama
Keyword(s):  
Phase Velocity ◽  
Speed Of Sound ◽  
Multiple Scales ◽  
Pure Water ◽  
Compressible Liquid ◽  
Nonlinear Propagation ◽  
Pure Liquid ◽  
Nls Equation ◽  
Very High Frequency ◽  
Weakly Nonlinear

Abstract The present paper theoretically treats weakly nonlinear propagation of plane progressive waves in an initially quiescent compressible liquid containing a tremendously large number of spherical gas bubbles, focusing on the derivation of an amplitude evolution equation (i.e., nonlinear wave equation). We emphasize the following points: (i) the compressibility of the liquid phase, which has long been neglected, is considered; (ii) the wave propagates with a large phase velocity exceeding the speed of sound in pure water; (iii) bubbles are not created or annihilated. From the method of multiple scales with an appropriate scaling of three nondimensional parameters, we can derive an attenuated nonlinear Schrödinger (NLS) equation, where the phase velocity is larger than the speed of sound in a pure liquid.

An Effect of Flow Velocity on Propagation Properties of Weakly Nonlinear Waves in Bubbly Flows

2019 ◽  
Author(s):  
Taiki Maeda ◽  
Tetsuya Kanagawa
Keyword(s):  
Multiple Scales ◽  
Fluid Model ◽  
Bubbly Flows ◽  
Nonlinear Propagation ◽  
Nonlinear Wave Equations ◽  
Nls Equation ◽  
Bubble Liquid ◽  
Weakly Nonlinear ◽  
Liquid Phases ◽  
Kdvb Equation

Abstract The present study theoretically carries out a derivation of the Korteweg–de Vries–Burgers (KdVB) equation and the nonlinear Schrödinger (NLS) equation for weakly nonlinear propagation of plane (i.e., one-dimensional) progressive waves in water flows containing many spherical gas bubbles that oscillate due to the pressure wave approaching the bubble. Main assumptions are as follows: (i) bubbly liquids are not at rest initially; (ii) the bubble does not coalesce, break up, extinct, and appear; (iii) the viscosity of the liquid phase is taken into account only at the bubble–liquid interface, although that of the gas phase is omitted; (iv) the thermal conductivities of the gas and liquid phases are dismissed. The basic equations for bubbly flows are composed of conservation equations for mass and momentum for the gas and liquid phases in a two-fluid model, the Keller-Miksis equation (i.e., the equation for radial oscillations as the expansion and contraction), and so on. By using the method of multiple scales and the determination of size of three nondimensional ratios that are wavelength, propagation speed and incident wave frequency, we can derive two types of nonlinear wave equations describing long range propagation of plane waves. One is the KdVB equation for a low frequency long wave, and the other is the NLS equation for an envelope wave for a moderately high frequency short carrier wave.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

scholarly journals Bubble Dynamics in a Two-Phase Bubbly Mixture

2010 ◽  
Author(s):  
Arvind Jayaprakash ◽  
Sowmitra Singh ◽  
Georges Chahine
Keyword(s):  
Void Fraction ◽  
High Speed ◽  
Bubble Dynamics ◽  
Bubble Radius ◽  
Discharge Voltage ◽  
Large Bubble ◽  
Water Mixture ◽  
Two Phase ◽  
Mixture Density ◽  
Bubbly Medium

The dynamics of a primary relatively large bubble in a water mixture including very fine bubbles is investigated experimentally and the results are provided to several parallel on-going analytical and numerical approaches. The main/primary bubble is produced by an underwater spark discharge from two concentric electrodes placed in the bubbly medium, which is generated using electrolysis. A grid of thin perpendicular wires is used to generate bubble distributions of varying intensities. The size of the main bubble is controlled by the discharge voltage, the capacitors size, and the pressure imposed in the container. The size and concentration of the fine bubbles can be controlled by the electrolysis voltage, the length, diameter, and type of the wires, and also by the pressure imposed in the container. This enables parametric study of the factors controlling the dynamics of the primary bubble and development of relationships between the bubble characteristic quantities such as maximum bubble radius and bubble period and the characteristics of the surrounding two-phase medium: micro bubble sizes and void fraction. The dynamics of the main bubble and the mixture is observed using high speed video photography. The void fraction/density of the bubbly mixture in the fluid domain is measured as a function of time and space using image analysis of the high speed movies. The interaction between the primary bubble and the bubbly medium is analyzed using both field pressure measurements and high-speed videography. Parameters such as the primary bubble energy and the bubble mixture density (void fraction) are varied, and their effects studied. The experimental data is then compared to simple compressible equations employed for spherical bubbles including a modified Gilmore Equation. Suggestions for improvement of the modeling are then presented.

Evaporation and Nucleate Boiling of an Individual Droplet on Surfaces

2005 ◽  
Author(s):  
X. D. Wang ◽  
G. Lu ◽  
X. F. Peng ◽  
B. X. Wang
Keyword(s):  
Heat Flux ◽  
High Speed ◽  
Bubble Dynamics ◽  
Imaging System ◽  
Dynamical Behavior ◽  
Saturation Temperature ◽  
Nucleate Boiling ◽  
Dynamical Process ◽  
Boiling Regime ◽  
Film Evaporation

A visual study was conducted to investigate the evaporation and nucleate boiling of a water droplet on heated copper, aluminum, or stainless surfaces with temperature ranging from 50°C to 112°C. Using a high-speed video imaging system, the dynamical process of the evaporation of a droplet was recoded to measure the transient variation of its diameter, height, and contact angle. When the contact temperature was lower than the saturation temperature, the evaporation was in film evaporation regime, and the evaporation could be divided into two stages. When the surface temperature was higher than the saturation temperature, the nucleate boiling was observed. The dynamical behavior of nucleation, bubble dynamics droplet were detail observed and discussed. The linear relationships of the average heat flux vs. temperature of the heated surfaces were found to hold for both the film evaporation regime and nucleate boiling regime. The different slopes indicated their heat transfer mechanism was distinct, the heat flux decreased in the nucleate boiling regime more rapidly than in the film evaporation due to the strong interaction between the bubbles.

Thermal Bubble Dynamics Under the Effect of Acoustic Vibration

2009 ◽  
Author(s):  
Xiaopeng Qu ◽  
Huihe Qiu
Keyword(s):  
Heat Transfer ◽  
Acoustic Field ◽  
Vapor Bubble ◽  
Boiling Heat Transfer ◽  
High Speed ◽  
Bubble Dynamics ◽  
Acoustic Vibration ◽  
Micro Electro Mechanical System ◽  
Mems Technology ◽  
Enhanced Boiling

The effect of acoustic field on the dynamics of micro thermal bubble is investigated in this paper. The micro thermal bubbles were generated by a micro heater which was fabricated by standard Micro-Electro-Mechanical-System (MEMS) technology and integrated into a mini chamber. The acoustic field formed in the mini chamber was generated by a piezoelectric plate which was adhered on the top side of the chamber’s wall. The dynamics and related heat transfer induced by the micro heater generated vapor bubble with and without the existing of acoustic field were characterized by a high speed photograph system and a micro temperature sensor. Through the experiments, it was found that in two different conditions, the temperature changing induced by the micro heater generated vapor bubble was significantly different. From the analysis of the high speed photograph results, the acoustic force induced micro thermal bubble movements, such as forcibly removing, collapsing and sweeping, were the main effects of acoustic enhanced boiling heat transfer. The experimental results and theoretical analysis were helpful for understanding of the mechanisms of acoustic enhanced boiling heat transfer and development of novel micro cooling devices.

Sign in / Sign up

Export Citation Format

Share Document