Density Ratio and Entrainment Effects on Asymptotic Rayleigh–Taylor Instability

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Assaf Shimony ◽  
Guy Malamud ◽  
Dov Shvarts
Keyword(s):  
Numerical Study ◽  
Density Ratio ◽  
Three Dimensional ◽  
Growth Parameter ◽  
Taylor Instability ◽  
Mixing Zone ◽  
Mixing Process ◽  
Mixing Parameters ◽  
Rayleigh Taylor Instability ◽  
Self Similar

A comprehensive numerical study was performed in order to examine the effect of density ratio on the mixing process inside the mixing zone formed by Rayleigh–Taylor instability (RTI). This effect exhibits itself in the mixing parameters and increase of the density of the bubbles. The motivation of this work is to relate the density of the bubbles to the growth parameter for the self-similar evolution, α, we suggest an effective Atwood formulation, found to be approximately half of the original Atwood number. We also examine the sensitivity of the parameters above to the dimensionality (two-dimensional (2D)/three-dimensional (3D)) and to numerical miscibility.

scholarly journals Transition stages of Rayleigh–Taylor instability between miscible fluids

2001 ◽  
Vol 443 ◽  
pp. 69-99 ◽  
Author(s):  
ANDREW W. COOK ◽  
PAUL E. DIMOTAKIS
Keyword(s):  
Growth Rates ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Taylor Instability ◽  
Initial Growth ◽  
Mixing Zone ◽  
Miscible Fluids ◽  
Rayleigh Taylor Instability

Direct numerical simulations (DNS) are presented of three-dimensional, Rayleigh–Taylor instability (RTI) between two incompressible, miscible fluids, with a 3:1 density ratio. Periodic boundary conditions are imposed in the horizontal directions of a rectangular domain, with no-slip top and bottom walls. Solutions are obtained for the Navier–Stokes equations, augmented by a species transport-diffusion equation, with various initial perturbations. The DNS achieved outer-scale Reynolds numbers, based on mixing-zone height and its rate of growth, in excess of 3000. Initial growth is diffusive and independent of the initial perturbations. The onset of nonlinear growth is not predicted by available linear-stability theory. Following the diffusive-growth stage, growth rates are found to depend on the initial perturbations, up to the end of the simulations. Mixing is found to be even more sensitive to initial conditions than growth rates. Taylor microscales and Reynolds numbers are anisotropic throughout the simulations. Improved collapse of many statistics is achieved if the height of the mixing zone, rather than time, is used as the scaling or progress variable. Mixing has dynamical consequences for this flow, since it is driven by the action of the imposed acceleration field on local density differences.

scholarly journals 3D Numerical simulation of Rayleigh–Taylor instability using MAH-3 code

2000 ◽  
Vol 18 (2) ◽  
pp. 175-181 ◽  
Author(s):  
N.N. ANUCHINA ◽  
V.I. VOLKOV ◽  
V.A. GORDEYCHUK ◽  
N.S. ES'KOV ◽  
O.S. IIYUTINA ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Numerical Study ◽  
Taylor Instability ◽  
Time Range ◽  
Similar Distribution ◽  
Flow Transition ◽  
Classical Energy ◽  
Rayleigh Taylor Instability ◽  
Self Similar

A 3D numerical study of the turbulent phase of the evolution of Rayleigh–Taylor instability (RTI) was undertaken using the MAH-3 code. A criterion and a technique have been developed that can be used for diagnostics in computational experiments studying flow transition to self-similar turbulence. It has been found that a criterion of the flow transition to the self-similar turbulence is Kolmogorov's self-similar distribution of the turbulent kinetic energy together with the square law of mixing zone extension. The technique is based on the analysis of the evolution of the dimensionless power spectrum of specific kinetic energy. Three phases of nonlinear mixing are found: “relict chaos”, “formation of classical energy spectrum” and “spectrum degradation.” Determination of a proportionality factor for a square law within the time range incorporating inertial interval gives the value of α ≈ 0.07.

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