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.

scholarly journals Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime

2018 ◽  
Vol 838 ◽  
pp. 320-355 ◽  
Author(s):  
R. V. Morgan ◽  
W. H. Cabot ◽  
J. A. Greenough ◽  
J. W. Jacobs
Keyword(s):  
Rarefaction Wave ◽  
Three Dimensional ◽  
Single Mode ◽  
Taylor Instability ◽  
Nonlinear Regime ◽  
Diffuse Interface ◽  
Late Time ◽  
Two Dimensional ◽  
Rayleigh Taylor Instability ◽  
Atwood Number

Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number, $A=(\unicode[STIX]{x1D70C}_{2}-\unicode[STIX]{x1D70C}_{1})/(\unicode[STIX]{x1D70C}_{2}+\unicode[STIX]{x1D70C}_{1})$, where $\unicode[STIX]{x1D70C}_{2}$ and $\unicode[STIX]{x1D70C}_{1}$ are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of $A=0.49$, $A=0.63$, $A=0.82$ and $A=0.94$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber, $k=2\unicode[STIX]{x03C0}/\unicode[STIX]{x1D706}=0.247~\text{mm}^{-1}$, experiments and simulations, where $\unicode[STIX]{x1D706}$ is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.

scholarly journals Experiments and Simulations on the Turbulent, Rarefaction Wave Driven Rayleigh–Taylor Instability

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
R. V. Morgan ◽  
J. W. Jacobs
Keyword(s):  
Rarefaction Wave ◽  
Lawrence Livermore National Laboratory ◽  
National Laboratory ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Diffuse Interface ◽  
Diffusion Layer Thickness ◽  
Average Value ◽  
Rayleigh Taylor Instability

Abstract Experiments were performed to observe the growth of the turbulent, Rayleigh–Taylor unstable mixing layer generated between air and SF6, with an Atwood number of A=(ρ2−ρ1)/(ρ2+ρ1)=0.64, where ρ1 and ρ2 are the densities of air and SF6, respectively. A nonconstant acceleration with an average value of 2300g0, where g0 is the acceleration due to gravity, was generated by interaction of the interface between the two gases with a rarefaction wave. Three-dimensional, multimode perturbations were generated on the diffuse interface, with a diffusion layer thickness of δ=3.6 mm, using a membraneless vertical oscillation technique, and 20 experiments were performed to establish a statistical ensemble. The average perturbation from this ensemble was extracted and used as input for a numerical simulation using the Lawrence Livermore National Laboratory (LLNL) Miranda code. Good qualitative agreement between the experiment and simulation was observed, while quantitative agreement was best at early to intermediate times. Several methods were used to extract the turbulent growth constant α from experiments and simulations while accounting for time varying acceleration. Experimental, average bubble and spike asymptotic self-similar growth rate values range from α=0.022 to α=0.032 depending on the method used, and accounting for variable acceleration. Values found from the simulations range from α=0.024 to α=0.041. Values of α measured in the experiments are lower than what are typically measured in the literature but are more in line with those found in recent simulations.

Rayleigh–Taylor instability of an inclined buoyant viscous cylinder

2011 ◽  
Vol 671 ◽  
pp. 313-338 ◽  
Author(s):  
JOHN R. LISTER ◽  
ROSS C. KERR ◽  
NICK J. RUSSELL ◽  
ANDREW CROSBY
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Maximum Growth ◽  
Propagation Rate ◽  
Taylor Instability ◽  
Polar Coordinates ◽  
Rayleigh Taylor Instability

The Rayleigh–Taylor instability of an inclined buoyant cylinder of one very viscous fluid rising through another is examined through linear stability analysis, numerical simulation and experiment. The stability analysis represents linear eigenmodes of a given axial wavenumber as a Fourier series in the azimuthal direction, allowing the use of separable solutions to the Stokes equations in cylindrical polar coordinates. The most unstable wavenumber k∗ is long-wave if both the inclination angle α and the viscosity ratio λ (internal/external) are small; for this case, k∗ ∝ max{α, (λ ln λ−1)1/2} and thus a small angle in experiments can have a significant effect for λ ≪ 1. As α increases, the maximum growth rate decreases and the upward propagation rate of disturbances increases; all disturbances propagate without growth if the cylinder is sufficiently close to vertical, estimated as α ≳ 70°. Results from the linear stability analysis agree with numerical calculations for λ = 1 and experimental observations. A point-force numerical method is used to calculate the development of instability into a chain of individual plumes via a complex three-dimensional flow. Towed-source experiments show that nonlinear interactions between neighbouring plumes are important for α ≳ 20° and that disturbances can propagate out of the system without significant growth for α ≳ 40°.

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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