scholarly journals Numerical and Experimental Analysis of the Growth of Gravitational Interfacial Instability Generated by Two Viscous Fluids of Different Densities

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Snehamoy Majumder ◽  
Debajit Saha ◽  
Partha Mishra
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Gravitational Instability ◽  
Physical Phenomenon ◽  
Taylor Instability ◽  
Interfacial Instability ◽  
Heaviside Function ◽  
Two Fluids ◽  
Gravity Driven ◽  
Rayleigh Taylor Instability

In the geophysical context, there are a wide variety of mechanisms which may lead to the formation of unstable density stratification, leading in turn to the development of the Rayleigh-Taylor instability and, more generally, interfacial gravity-driven instabilities, which involves moving boundaries and interfaces. The purpose of this work is to study the level set method and to apply the process to study the Rayleigh-Taylor instability experimentally and numerically. With the help of a simple, inexpensive experimental arrangement, the R-T instability has been visualized with moderate accuracy for real fluids. The same physical phenomenon has been investigated numerically to track the interface of two fluids of different densities to observe the gravitational instability with the application of level set method coupled with volume of fraction replacing the Heaviside function. Good agreement between theory and experimental results was found and growth of instability for both of the methods has been plotted.

NUMERICAL SIMULATION OF RAYLEIGH–TAYLOR INSTABILITY BASED ON AN IMPROVED PARTICLE LEVEL SET METHOD

2014 ◽  
Vol 11 (04) ◽  
pp. 1350094 ◽  
Author(s):  
HUI TIAN ◽  
GUOJUN LI ◽  
XIONGWEN ZHANG
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Density Ratio ◽  
Immiscible Fluids ◽  
Taylor Instability ◽  
Wide Range ◽  
Particle Level ◽  
Rayleigh Taylor Instability ◽  
Particle Level Set Method

An improved particle correction procedure for particle level set method is proposed and applied to the simulation of Rayleigh–Taylor instability (RTI) of the incompressible two-phase immiscible fluids. In the proposed method, an improved particle correction method is developed to deal with all the relative positions between escaped particles and cell corners, which can reduce the disturbance arising in the distance function correction process due to the non-normal direction movement of escaped particles. The improved method is validated through accurately capturing the moving interface of the Zalesak's disk. Furthermore, coupled with the projection method for solving the Navier–Stokes equations, the time-dependent evolution of the RTI interface over a wide range of Reynolds numbers, Atwood numbers and Weber numbers are numerically investigated. A good agreement between the present results and the existing analytical solutions is obtained and the accuracy of the proposed method is further verified. Moreover, the effects of control parameters including viscosity, density ratio, and surface tension coefficient on the evolution of RTI are analyzed in detail, and a critical Weber number for the development of RTI is found.

Simulation of Multi-Mode Film Boiling Using Level Set Method

2009 ◽  
Author(s):  
Vinesh H. Gada ◽  
Atul Sharma
Keyword(s):  
Film Thickness ◽  
Level Set ◽  
Taylor Instability ◽  
Viscous Force ◽  
Film Boiling ◽  
Inertia Force ◽  
Initial Film ◽  
Wall Superheat ◽  
Rayleigh Taylor Instability ◽  
Multi Mode

2D transient multi-mode film boiling simulation of water near critical pressure (p = 0.99pc = 21.9 MPa) on a heated horizontal surface is carried out using an in-house Level Set (LS) method based semi-explicit finite volume method code. The influence of initial vapor film thickness (yo) on the dominant instability mode is evaluated by carrying out simulations on domain having width greater than most dangerous Taylor wavelength i.e. LX = 4λd with y0 = 0.0425λd and 0.125λd at low wall superheat (ΔT = 2K). For lower initial film thickness, the viscous force dominated Rayleigh-Taylor instability is captured and the average bubble spacing is found close to the prediction made using lubrication theory i.e. λP = 2λc = 0.816λd. However, for higher initial film thickness, the inertia force dominated Taylor-Helmholtz mode of instability is found with the average bubble spacing close to λd. Simulations are carried out to check the existence of Rayleigh-Taylor instability on various domain width LX = 2λd, 3λd, 4λd and 6λd at yo = 0.0425λd and ΔT = 2K. The average bubble spacing for all domain widths is found to be less than 2λc indicating that the Rayleigh-Taylor instability is dominant.

scholarly journals Experimental investigation into inertial properties of Rayleigh–Taylor turbulence

1997 ◽  
Vol 15 (1) ◽  
pp. 25-31 ◽  
Author(s):  
Yu.A. Kucherenko ◽  
S.I. Balabin ◽  
R. Cherret ◽  
J.F. Haas
Keyword(s):  
Experimental Investigation ◽  
Kinetic Energy ◽  
Turbulent Mixing ◽  
Average Density ◽  
Taylor Instability ◽  
X Ray ◽  
Two Fluids ◽  
Time Space ◽  
Rayleigh Taylor Instability ◽  
Region Size

An experimental investigation into inertial properties of the developed Rayleigh–Taylor instability with the different initial values of the kinetic energy of turbulence has been performed. The experiments were performed by using two fluids having different densities with density ration n = 3. Fluids were placed in an ampoule. At the unstable stage of motion, the ampoule was moving under an acceleration. At a certain instant of time the acceleration was removed and the ampoule moved under the force of inertia. By means of pulsed X-ray photography, the mixing region size and the time-space distributionof the average density of matter in the turbulent mixing region have been determined at different instants of time. The time-space distributions are compared with those obtained by semiempirical theories of mixing.

Numerical studies of some nonlinear hydrodynamic problems by discrete vortex element methods

1978 ◽  
Vol 84 (3) ◽  
pp. 433-453 ◽  
Author(s):  
J. C. S. Meng ◽  
J. A. L. Thomson
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Gravity Current ◽  
Vortex Sheet ◽  
Taylor Instability ◽  
Green’S Function Method ◽  
Discrete Vortex ◽  
Two Fluids ◽  
Rayleigh Taylor Instability

A class of nonlinear hydrodynamic problems is studied. Physical problems such as shear flow, flow with a sharp interface separating two fluids of different density and flow in a porous medium all belong to this class. Owing to the density difference across the interface, vorticity is generated along it by the interaction between the gravitational pressure gradient and the density gradient, and the motion consists of essentially two processes: the creation of a vortex sheet and the subsequent mutual induction of different portions of this sheet.Two numerical methods are investigated. One is based upon the well-known Green's function method, which is a Lagrangian method using the Biot-Savart law, while the other is the vortex-in-cell (VIC) method, which is a Lagrangian-Eulerian method. Both methods treat the interface as sharp and represent it by a distribution of point vortices. The VIC method applies the FFT (fast Fourier transform) to solve the stream-function/vorticity equation on an Eulerian grid, and computational efficiency is further improved by using the reality properties of the physical variables.Four specific problems are investigated numerically in this paper. They are: the Rayleigh-Taylor instability, the Saffman-Taylor instability, transport of aircraft trailing vortices in a wind shear, and the gravity current. All four problems are solved using the VIC method and the results agree well with results obtained by previous investigators. The first two problems, the Rayleigh-Taylor instability and the Saffman-Taylor instability, are also solved by the Green's function method. Comparisons of results obtained by the two methods show good agreement, but, owing to its computational economy, the VIC method is concluded to be the better method for treating the class of hydrodynamic problems considered here.

Effects of Heat and Mass Transfer on Rayleigh-Taylor Instability

1972 ◽  
Vol 94 (1) ◽  
pp. 156-160 ◽  
Author(s):  
D. Y. Hsieh
Keyword(s):  
Mass Transfer ◽  
Phase Transformation ◽  
Dispersion Relation ◽  
Temperature Gradient ◽  
Thermal Effect ◽  
Taylor Instability ◽  
Interfacial Wave ◽  
Interfacial Conditions ◽  
Two Fluids ◽  
Rayleigh Taylor Instability

The effect on the interfacial gravity wave between two fluids is studied when there is a temperature gradient in the fluids. It is found that the thermal effect is closely related to the phase transformation across the interface. The interfacial conditions with mass flow are first derived. Then the dispersion relation for the interfacial wave is obtained. It is found that the effect of evaporation is to damp the interfacial wave and to enhance the Rayleigh-Taylor instability. It is also found that the system will be stabilized or destabilized depending on whether the vapor is hotter or colder than the liquid.

scholarly journals Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface

2014 ◽  
Vol 6 (2) ◽  
pp. 1523-1554 ◽  
Author(s):  
B. Hillebrand ◽  
C. Thieulot ◽  
T. Geenen ◽  
A. P. van den Berg ◽  
W. Spakman
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Material Flow ◽  
Flow Modeling ◽  
Material Interfaces ◽  
Level Set Function ◽  
Geophysical Processes ◽  
Rayleigh Taylor Instability ◽  
Set Function

Abstract. The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is well suited for applications of multi-material flow modeling. The level set method utilizes smooth level set functions to define material interfaces, which makes the method stable and free of oscillations that are typically observed in case step-like functions parameterize interfaces. By design the level set function is a signed distance function and gives for each point in the domain the exact distance to the interface and on which side it is located. In this paper we present four benchmarks which show the validity, accuracy and simplicity of using the level set method for multi-material flow modeling. The benchmarks are simplified setups of dynamical geophysical processes such as a Rayleigh–Taylor instability, post glacial rebound, subduction and slab detachment. We also demonstrate the benefit of using the level set method for modeling a free surface with the sticky air approach. Our results show that the level set method allows for accurate material flow modeling and that the combination with the sticky air approach works well in mimicking Earth's free surface. Since the level set method tracks material interfaces instead of materials themselves, it has the advantage that the location of these interfaces is accurately known and that it represents a viable alternative to the more commonly used tracer method.

Landau Quantised Modification of Rayleigh–Taylor Instability in Dense Plasmas

2020 ◽  
Vol 75 (2) ◽  
pp. 113-118 ◽  
Author(s):  
M. Shahid ◽  
A. Rasheed ◽  
Misbah Kanwal ◽  
M. Jamil
Keyword(s):  
Magnetic Field ◽  
Gravitational Instability ◽  
Taylor Instability ◽  
Dense Plasmas ◽  
Exchange Correlation ◽  
Quantum Hydrodynamic Model ◽  
Exchange Correlation Potential ◽  
Correlation Potential ◽  
Rayleigh Taylor Instability ◽  
Quantum Hydrodynamic

AbstractEffects of Landau quantisation and exchange-correlation potential on Rayleigh–Taylor instability (RTI)/gravitational instability are investigated in inhomogeneous dense plasmas. Quantum hydrodynamic model is used for the electrons, while the ions are assumed to be cold and classical. RTI is modified with the inclusion of Landau quantisation related to plasma density, ambient magnetic field, exchange speed, and modified Fermi speed. Owing to the exchange-correlation effects, gravitational instability increases, whereas the Landau quantisation effects contribute in the opposite way for quantisation factor η < 1. Since the exchange-correlation potential is a function of density, by controlling the number density and magnetic field one can control RTI.

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