Nonlinear Oscillations of a Spherically Symmetric Single Bubble in an Acoustic Field

2011 ◽  
Vol 8 (1) ◽  
pp. 45-53
Author(s):  
E.V. Volkova ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Mass Transfer ◽  
Acoustic Field ◽  
Moving Boundary ◽  
Nonlinear Oscillations ◽  
Diffusion Problem ◽  
Spherically Symmetric ◽  
Lagrangian Coordinates ◽  
Gas Bubble ◽  
Bubble Wall ◽  
Convection Diffusion

In the present paper the dynamics of a single gas bubble under the influence of an acoustic field is studied, taking mass transfer through the moving bubble wall into account. Mass transfer is calculated separately in the diffusion problem. Due to changes in the pressure inside the bubble caused by oscillations of its volume, the concentration of the gas dissolved in the liquid undergoes oscillations of large amplitude near the bubble boundary. To eliminate the computational problems associated with the moving boundary, the convection-diffusion equations describing the transport of a gas dissolved in a liquid are written in Lagrangian coordinates.

Conservative Scheme Application for the Numerical Modeling of the Diffusion Problem for a Single Bubble in an Acoustic Field

2014 ◽  
Vol 10 ◽  
pp. 32-37
Author(s):  
E.V. Butyugina ◽  
E.Sh. Nasibullaeva ◽  
I.Sh. Akhatov ◽  
N.A. Gumerov
Keyword(s):  
Nonlinear Dynamics ◽  
Acoustic Field ◽  
Total Mass ◽  
Numerical Scheme ◽  
Diffusion Flux ◽  
Liquid System ◽  
Diffusion Problem ◽  
Gas Bubble ◽  
Conservative Scheme ◽  
Strongly Nonlinear

In the present study a numerical method for simulation of the diffusion problem for a single gas bubble oscillating in an acoustic field is developed. The method is based on the conservative numerical scheme for the diffusion equation where diffusion flux continuity is acting as conservation law. This method allows one to take into account the influence of changing mass of the gas inside the bubble on the strongly nonlinear dynamics of a bubble. The numerical results obtained using the proposed method utilizing conservative scheme and the standard scheme, which does not conserve the total mass of the gas-liquid system, reveals that in the latter case the numerical error may accumulate and lead to physically incorrect results.

Analysis of the diffusion influence on the bubble dynamics in an acoustic field

2012 ◽  
Vol 9 (1) ◽  
pp. 53-58
Author(s):  
E.V. Volkova ◽  
E.Sh. Nasibullaeva ◽  
I.Sh. Akhatov
Keyword(s):  
Numerical Method ◽  
Acoustic Field ◽  
Numerical Experiments ◽  
Bubble Dynamics ◽  
External Pressure ◽  
Diffusion Problem ◽  
Spherically Symmetric ◽  
Calculation Results ◽  
Cluster A ◽  
Parallelization Efficiency

A diffusion problem for a spherically symmetric gas bubble in a liquid in an isotropic acoustic field is considered. The problem is solved both for a single bubble and for a bubble in a monodisperse cluster. A numerical method for solving the diffusion problem is developed. For the oscillating part of the diffusion problem the numerical experiments have been carried out for different amplitudes of the external pressure. A comparison is made between the calculation results obtained by the approximation theory and the numerical method presented. The effect of taking into account the mass change on the bubble dynamics is studied. For extensive parametric research the algorithm is paralleled and the parallelization efficiency is evaluated.

MULTIPLE-SCALE AND NUMERICAL ANALYSES FOR THE NONLINEAR OSCILLATIONS OF A GAS BUBBLE SURROUNDED BY A MAXWELL'S FLUID

2019 ◽  
Vol 46 (3) ◽  
pp. 261-275
Author(s):  
César Yepes ◽  
Jorge Naude ◽  
Federico Mendez ◽  
Margarita Navarrete ◽  
Fátima Moumtadi
Keyword(s):  
Nonlinear Oscillations ◽  
Multiple Scale ◽  
Numerical Analyses ◽  
Gas Bubble

scholarly journals A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

scholarly journals A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 769-782
Author(s):  
Amiya K. Pani ◽  
Vidar Thomée ◽  
A. S. Vasudeva Murthy
Keyword(s):  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Second Order ◽  
Time Step ◽  
Convection Diffusion ◽  
First Order ◽  
Backward Euler ◽  
Strang Splitting ◽  
Spatially Periodic

AbstractWe analyze a second-order in space, first-order in time accurate finite difference method for a spatially periodic convection-diffusion problem. This method is a time stepping method based on the first-order Lie splitting of the spatially semidiscrete solution. In each time step, on an interval of length k, of this solution, the method uses the backward Euler method for the diffusion part, and then applies a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {\frac{k}{m}} for the convection part. With h the mesh width in space, this results in an error bound of the form {C_{0}h^{2}+C_{m}k} for appropriately smooth solutions, where {C_{m}\leq C^{\prime}+\frac{C^{\prime\prime}}{m}}. This work complements the earlier study [V. Thomée and A. S. Vasudeva Murthy, An explicit-implicit splitting method for a convection-diffusion problem, Comput. Methods Appl. Math. 19 2019, 2, 283–293] based on the second-order Strang splitting.

The Effect of Shear Flow and Dissolved Gas Diffusion on the Cavitation in a Submerged Journal Bearing

2000 ◽  
Vol 123 (3) ◽  
pp. 494-500 ◽  
Author(s):  
M. Groper ◽  
I. Etsion
Keyword(s):  
Mass Transfer ◽  
Shear Flow ◽  
Mass Transport ◽  
Transport Mechanism ◽  
Journal Bearing ◽  
Gas Diffusion ◽  
Gas Bubble ◽  
Dissolved Gas ◽  
Rotating Shaft ◽  
Mass Transfer Mechanism

Two possible, long standing speculated mechanisms are theoretically investigated in an attempt to understand previous experimental observations of pressure build up in the cavitation zone of a submerged journal bearing. These mechanisms are (1) the shear of the cavity gas bubble by a thin lubricant film dragged through the cavitation zone by the rotating shaft and (2) the mass transfer mechanism which dictates the rate of diffusion of dissolved gas out of and back into the lubricant. A comparison with available experimental results reveals that while the cavitation shape is fairly well predicted by the “shear” mechanism, this mechanism is incapable of generating the level of the experimentally measured pressures, particularly towards the end of the cavitation zone. The “mass transport” mechanism is found inadequate to explain the experimental observations. The effect of this mechanism on the pressure build up in the cavitation zone can be completely ignored.

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