Lattice Boltzmann simulation of three-dimensional Rayleigh-Taylor instability

Area of Science:

• Fluid Dynamics
• Computational Physics
• Multiphase Flow

Background:

• The Rayleigh-Taylor instability (RTI) is a fundamental phenomenon in fluid dynamics.
• Understanding RTI is crucial for various applications, including inertial confinement fusion and astrophysical processes.
• Previous studies have primarily focused on 2D simulations or higher Atwood numbers.

Purpose of the Study:

• To investigate the three-dimensional Rayleigh-Taylor instability (RTI) in a square duct with a low Atwood number (A(t)=0.15).
• To analyze the effect of Reynolds number on interfacial dynamics, bubble, and spike amplitudes.
• To explore the late-time behavior and topological structures of the RTI.

Main Methods:

• Utilized a multiple-relaxation-time lattice Boltzmann (LB) multiphase model for 3D simulations.
• Investigated a long square duct geometry (12W × W × W).
• Employed Graphics Processing Unit (GPU) parallel computing to handle computational costs.

Main Results:

• At high Reynolds numbers, RTI exhibits distinct stages: linear growth, terminal velocity, reacceleration, and chaotic development.
• Complex interface topologies and dissociative drops were observed at late stages.
• Bubble and spike velocities exceeded potential flow theory predictions, with normalized acceleration fluctuating around 0.16.
• At low Reynolds numbers, later stages were not reached, interfaces remained smooth, and bubble velocity approached a constant, aligning with extended Layzer and modified potential theories.

Conclusions:

• Reynolds number significantly influences the progression and complexity of 3D RTI.
• The LB model accurately captures the transition from ordered to chaotic interfacial dynamics.
• Simulation results provide valuable data for validating theoretical models of RTI at low Atwood numbers.