Asymptotic model of the axisymmetric breakdown of a vortex filament in an incompressible fluid

1990 ◽  
Vol 24 (6) ◽  
pp. 862-867
Author(s):  
A. V. Zubtsov
Keyword(s):  
Incompressible Fluid ◽  
Vortex Filament ◽  
Asymptotic Model

scholarly journals The motion of a buoyant vortex filament

2018 ◽  
Vol 857 ◽  
Author(s):  
Ching Chang ◽  
Stefan G. Llewellyn Smith
Keyword(s):  
Analytic Solution ◽  
Axial Flow ◽  
External Pressure ◽  
Transverse Component ◽  
Tangential Component ◽  
Force Balance ◽  
Vortex Filament ◽  
Vortex Rings ◽  
Asymptotic Model ◽  
Vortex Element

We investigate the motion of a thin vortex filament in the presence of buoyancy. The asymptotic model of Moore & Saffman (Phil. Trans. R. Soc. Lond.A, vol. 272, 1972, pp. 403–429) is extended to take account of buoyancy forces in the force balance on a vortex element. The motion of a buoyant vortex is given by the transverse component of force balance, while the tangential component governs the dynamics of the structure in the core. We show that the local acceleration of axial flow is generated by the external pressure gradient due to gravity. The equations are then solved for vortex rings. An analytic solution for a buoyant vortex ring at a small initial inclination is obtained and asymptotically agrees with the literature.

Non-stationary process characteristics of the gas outflow into a liquid

2019 ◽  
Vol 14 (2) ◽  
pp. 82-88
Author(s):  
M.V. Alekseev ◽  
I.S. Vozhakov ◽  
S.I. Lezhnin
Keyword(s):  
Numerical Simulation ◽  
Liquid Column ◽  
Gas Content ◽  
Liquid Lead ◽  
Gas Flows ◽  
Asymptotic Model ◽  
Process Characteristics ◽  
Significant Difference ◽  
Order Of Magnitude ◽  
Volume Method

A numerical simulation of the process of the outflow of gas under pressure into a closed container partially filled with liquid was carried out. For comparative theoretical analysis, an asymptotic model was used with assumptions about the adiabaticity of the gas outflow process and the ideality of the liquid during the oscillatory one-dimensional motion of the liquid column. In this case, the motion of the liquid column and the evolution of pressure in the gas are determined by the equation of dynamics and the balance of enthalpy. Numerical simulation was performed in the OpenFOAM package using the fluid volume method (VOF method) and the standard k-e turbulence model. The evolution of the fields of volumetric gas content, velocity, and pressure during the flow of gas from the high-pressure chamber into a closed channel filled with liquid in the presence of a ”gas blanket“ at the upper end of the channel is obtained. It was shown that the dynamics of pulsations in the gas cavity that occurs when the gas flows into the closed region substantially depends on the physical properties of the liquid in the volume, especially the density. Numerical modeling showed that the injection of gas into water occurs in the form of a jet outflow of gas, and for the outflow into liquid lead, a gas slug is formed at the bottom of the channel. Satisfactory agreement was obtained between the numerical calculation and the calculation according to the asymptotic model for pressure pulsations in a gas projectile in liquid lead. For water, the results of calculations using the asymptotic model give a significant difference from the results of numerical calculations. In all cases, the velocity of the medium obtained by numerical simulation and when using the asymptotic model differ by an order of magnitude or more.

Lattice-BGK Methods for Simulating Incompressible Fluid Flows

1997 ◽  
Vol 08 (04) ◽  
pp. 793-803 ◽  
Author(s):  
Yu Chen ◽  
Hirotada Ohashi
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
General Model ◽  
Incompressible Flows ◽  
Fluid Flows ◽  
Incompressible Limit ◽  
Numerical Example ◽  
Incompressible Fluid Flows

The lattice-Bhatnagar-Gross-Krook (BGK) method has been used to simulate fluid flow in the nearly incompressible limit. But for the completely incompressible flows, two special approaches should be applied to the general model, for the steady and unsteady cases, respectively. Introduced by Zou et al.,1 the method for steady incompressible flows will be described briefly in this paper. For the unsteady case, we will show, using a simple numerical example, the need to solve a Poisson equation for pressure.

Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a sheared magnetic field

1990 ◽  
Vol 44 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Hiromitsu Hamabata
Keyword(s):  
Magnetic Field ◽  
Incompressible Fluid ◽  
Large Amplitude ◽  
Uniform Magnetic Field ◽  
Magnetohydrodynamic Equations ◽  
Wave Solutions ◽  
Field Lines ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Physical Quantities ◽  
Nonlinear Wave Solutions

Exact wave solutions of the nonlinear jnagnetohydrodynamic equations for a highly conducting incompressible fluid are obtained for the cases where the physical quantities are independent of one Cartesian co-ordina.te and for where they vary three-dimensionally but both the streamlines and magnetic field lines lie in parallel planes. It is shown that there is a class of exact wave solutions with large amplitude propagating in a straight but non-uniform magnetic field with constant or non-uniform velocity.

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