scholarly journals Fully 3D Rayleigh-Taylor instability in a Boussinesq fluid

2019 ◽  
Vol 61 ◽  
pp. 286-304
Author(s):  
Stephen John Walters ◽  
Lawrence K. Forbes
Keyword(s):  
Numerical Calculation ◽  
Spectral Method ◽  
Large Scale ◽  
Three Dimensional ◽  
Early Time ◽  
Taylor Instability ◽  
3D Geometry ◽  
Linearized Theory ◽  
Rayleigh Taylor Instability ◽  
Boussinesq Fluid

Rayleigh–Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present a linearized theory for arbitrary three-dimensional (3D) initial disturbances that grow in time, and calculate the evolution of the interface for early times. A new spectral method is introduced for the fully 3D nonlinear problem in a Boussinesq fluid, where the interface between the light and heavy fluids is approximated with a smooth but rapid density change in the fluid. The results of large-scale numerical calculation are presented in fully 3D geometry, and compared and contrasted with the early-time linearized theory. doi:10.1017/S1446181119000087

scholarly journals FULLY 3D RAYLEIGH–TAYLOR INSTABILITY IN A BOUSSINESQ FLUID

2019 ◽  
Vol 61 (3) ◽  
pp. 286-304 ◽  
Author(s):  
S. J. WALTERS ◽  
L. K. FORBES
Keyword(s):  
Numerical Calculation ◽  
Spectral Method ◽  
Large Scale ◽  
Three Dimensional ◽  
Early Time ◽  
Taylor Instability ◽  
3D Geometry ◽  
Linearized Theory ◽  
Rayleigh Taylor Instability ◽  
Boussinesq Fluid

Rayleigh–Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present a linearized theory for arbitrary three-dimensional (3D) initial disturbances that grow in time, and calculate the evolution of the interface for early times. A new spectral method is introduced for the fully 3D nonlinear problem in a Boussinesq fluid, where the interface between the light and heavy fluids is approximated with a smooth but rapid density change in the fluid. The results of large-scale numerical calculation are presented in fully 3D geometry, and compared and contrasted with the early-time linearized theory.

scholarly journals On the “Early-Time” Evolution of Variables Relevant to Turbulence Models for the Rayleigh-Taylor Instability

2010 ◽  
Author(s):  
Bertrand Rollin ◽  
Malcolm J. Andrews
Keyword(s):  
Turbulence Model ◽  
Initial Conditions ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Early Time ◽  
Variable Density ◽  
Taylor Instability ◽  
Turbulent Regime ◽  
Rayleigh Taylor Instability

We present our progress toward setting initial conditions in variable density turbulence models. In particular, we concentrate our efforts on the BHR turbulence model [1] for turbulent Rayleigh-Taylor instability. Our approach is to predict profiles of relevant variables before fully turbulent regime and use them as initial conditions for the turbulence model. We use an idealized model of mixing between two interpenetrating fluids to define the initial profiles for the turbulence model variables. Velocities and volume fractions used in the idealized mixing model are obtained respectively from a set of ordinary differential equations modeling the growth of the Rayleigh-Taylor instability and from an idealization of the density profile in the mixing layer. A comparison between predicted profiles for the turbulence model variables and profiles of the variables obtained from low Atwood number three dimensional simulations show reasonable agreement.

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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