Lattice Boltzmann simulation of the Rayleigh–Taylor Instability (RTI) during the mixing of the immiscible fluids

The Rayleigh–Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method, the sharp fluid interface is replaced by a thin, yet finite, transition layer where the interfacial forces vary smoothly. This is achieved by introducing an order parameter (the phase-field) continuously varying across the interfacial layers and uniform in the bulk region. The phase-field model obeys a Cahn–Hilliard equation and is two-way coupled to the standard Navier–Stokes equations. Starting from this system of equations we have first performed a linear analysis from which we have analytically rederived the known gravity–capillary dispersion relation in the limit of vanishing mixing energy density and capillary width. We have performed numerical simulations and identified a region of parameters in which the known properties of the linear phase (both stable and unstable) are reproduced in a very accurate way. This has been done both in the case of negligible viscosity and in the case of non-zero viscosity. In the latter situation, only upper and lower bounds for the perturbation growth rate are known. Finally, we have also investigated the weakly nonlinear stage of the perturbation evolution and identified a regime characterized by a constant terminal velocity of bubbles/spikes. The measured value of the terminal velocity is in agreement with available theoretical prediction. The phase-field approach thus appears to be a valuable technique for the dynamical description of the stages where hydrodynamic turbulence and wave-turbulence come into play.

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

International Journal of Computational Methods ◽

10.1142/s0219876213500941 ◽

2014 ◽

Vol 11 (04) ◽

pp. 1350094 ◽

Cited By ~ 1

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.

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Lattice Boltzmann Simulation of Particle Motion in Binary Immiscible Fluids

Communications in Computational Physics ◽

10.4208/cicp.101114.150415a ◽

2015 ◽

Vol 18 (3) ◽

pp. 757-786 ◽

Cited By ~ 15

Author(s):

Yu Chen ◽

Qinjun Kang ◽

Qingdong Cai ◽

Moran Wang ◽

Dongxiao Zhang

Keyword(s):

Lattice Boltzmann ◽

Particle Motion ◽

Mass Conservation ◽

Immiscible Fluids ◽

Lattice Boltzmann Model ◽

Lattice Boltzmann Simulation ◽

Suspension Model ◽

Wetting Model ◽

Boltzmann Model ◽

The Impact

AbstractWe combine the Shan-Chen multicomponent lattice Boltzmann model and the link-based bounce-back particle suspension model to simulate particle motion in binary immiscible fluids. The impact of the slightly mixing nature of the Shan-Chen model and the fluid density variations near the solid surface caused by the fluid-solid interaction, on the particle motion in binary fluids is comprehensively studied. Our simulations show that existing models suffer significant fluid mass drift as the particle moves across nodes, and the obtained particle trajectories deviate away from the correct ones. A modified wetting model is then proposed to reduce the non-physical effects, and its effectiveness is validated by comparison with existing wetting models. Furthermore, the first-order refill method for the newly created lattice node combined with the new wetting model significantly improves mass conservation and accuracy.

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Lattice Boltzmann simulation of viscous fingering phenomenon of immiscible fluids displacement in a channel

Computers & Fluids ◽

10.1016/j.compfluid.2009.12.005 ◽

2010 ◽

Vol 39 (5) ◽

pp. 768-779 ◽

Cited By ~ 46

Author(s):

Bo Dong ◽

Y.Y. Yan ◽

Weizhong Li ◽

Yongchen Song

Keyword(s):

Lattice Boltzmann ◽

Viscous Fingering ◽

Immiscible Fluids ◽

Lattice Boltzmann Simulation

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

International Journal of Modern Physics C ◽

10.1142/s0129183109014746 ◽

2009 ◽

Vol 20 (11) ◽

pp. 1803-1816 ◽

Cited By ~ 15

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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