Rayleigh-Taylor instability of a thin liquid layer in the presence of three-dimensional perturbations

1999 ◽  
Vol 40 (1) ◽  
pp. 1-5
Author(s):  
S. M. Bakhrakh ◽  
G. P. Simonov
Keyword(s):  
Liquid Layer ◽  
Three Dimensional ◽  
Taylor Instability ◽  
Thin Liquid Layer ◽  
Rayleigh Taylor Instability

scholarly journals Studies of Rayleigh–Taylor instability of a thin liquid layer

1997 ◽  
Vol 15 (1) ◽  
pp. 93-99
Author(s):  
S.M. Bakhrakh ◽  
G.P. Simonov
Keyword(s):  
Liquid Layer ◽  
Complete System ◽  
Analytic Solutions ◽  
Taylor Instability ◽  
Numerical Calculations ◽  
Thin Liquid Layer ◽  
Instability Problem ◽  
Oscillating Solutions ◽  
Layer Velocity ◽  
Rayleigh Taylor Instability

On the basis of Lagrangian representation for equation of thin-liquid-layer dynamics, analytic solutions of the Rayleigh–Taylor instability problem at the nonlinear stage in the observer's space are found. Evolution of various perturbation types, in the layer shape and in layer velocity components, is considered. It is shown that there are both exponentially growing and limited oscillating solutions. The results of the theoretic considerations are substantiated with numerical calculations that use the complete system of the law of conservation.

scholarly journals Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

2016 ◽  
Vol 791 ◽  
pp. 34-60 ◽  
Author(s):  
R. V. Morgan ◽  
O. A. Likhachev ◽  
J. W. Jacobs
Keyword(s):  
Linear Stability ◽  
Rarefaction Wave ◽  
Diffusion Model ◽  
Growth Rates ◽  
Three Dimensional ◽  
Mie Scattering ◽  
Taylor Instability ◽  
Diffuse Interface ◽  
Rayleigh Taylor Instability ◽  
Dynamic Diffusion

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order of $1000g_{0}$, where $g_{0}$ is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duff et al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duff et al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a $1/k^{2}$ decay in growth rates as $k\rightarrow \infty$ for large-wavenumber perturbations.

APPLICATIONS OF FINITE-DIFFERENCE LATTICE BOLTZMANN METHOD TO BREAKUP AND COALESCENCE IN MULTIPHASE FLOWS

2009 ◽  
Vol 20 (11) ◽  
pp. 1803-1816 ◽  
Author(s):  
DANIELE CHIAPPINI ◽  
GINO BELLA ◽  
SAURO SUCCI ◽  
STEFANO UBERTINI
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann ◽  
Multiphase Flows ◽  
Liquid Droplet ◽  
Three Dimensional ◽  
Taylor Instability ◽  
Droplet Breakup ◽  
Lattice Boltzmann Model ◽  
Test Case ◽  
Rayleigh Taylor Instability

We present an application of the hybrid finite-difference Lattice-Boltzmann model, recently introduced by Lee and coworkers for the numerical simulation of complex multiphase flows.1–4 Three typical test-case applications are discussed, namely Rayleigh–Taylor instability, liquid droplet break-up and coalescence. The numerical simulations of the Rayleigh–Taylor instability confirm the capability of Lee's method to reproduce literature results obtained with previous Lattice-Boltzmann models for non-ideal fluids. Simulations of two-dimensional droplet breakup reproduce the qualitative regimes observed in three-dimensional simulations, with mild quantitative deviations. Finally, the simulation of droplet coalescence highlights major departures from the three-dimensional picture.

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