Lattice Boltzmann Solver for Multiphase Flows: Application to High Weber and Reynolds Numbers

Abstract

The lattice Boltzmann method, now widely used for a variety of applications, has also been extended to model multiphase flows through different formulations. While already applied to many different configurations in low Weber and Reynolds number regimes, applications to higher Weber/Reynolds numbers or larger density/viscosity ratios are still the topic of active research. In this study, through a combination of a decoupled phase-field formulation—the conservative Allen–Cahn equation—and a cumulant-based collision operator for a low-Mach pressure-based flow solver, we present an algorithm that can be used for higher Reynolds/Weber numbers. The algorithm was validated through a variety of test cases, starting with the Rayleigh–Taylor instability in both 2D and 3D, followed by the impact of a droplet on a liquid sheet. In all simulations, the solver correctly captured the flow dynamics andmatched reference results very well. As the final test case, the solver was used to model droplet splashing on a thin liquid sheet in 3D with a density ratio of 1000 and kinematic viscosity ratio of 15, matching the water/air system at We = 8000 and Re = 1000. Results showed that the solver correctly captured the fingering instabilities at the crown rim and their subsequent breakup, in agreement with experimental and numerical observations reported in the literature.

Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh–Taylor system

“…Such extension of the present GPU code can be a non-trivial task. This extension may also be achieved by using some other lattice Boltzmann methods based on phase-field models or the colour gradient method, such as in the works [19,20,30,32], where the algorithms are employed in conjunction with MRT or central moments based algorithms.…”

“…Despite this limitation, considerable advances in numerical simulations of the RT instability have been verified in the last decades, especially in the context of systems with miscible fluids [6][7][8][9][10][11][12]. Fewer works have been dedicated to the immiscible two-dimensional (2D) viscous case [1,[13][14][15][16][17][18][19][20], and most of them are devoted to the early stages of the instability with little information about the state of developed turbulence. Only recently, the 2D immiscible RT instability was simulated for high Reynolds numbers [17,18,[21][22][23].…”

Toward pore-scale simulation of combustion in porous media using a low-Mach hybrid lattice Boltzmann/finite-difference solver

“…In the context of the present study, following our proposals for both multi-phase and multi-species flows, 28,31 the Cumulants-based operator is used. 32 The post-collision populations g à i are computed as…”

Lattice-Boltzmann modeling of buoyancy-driven turbulent flows

“…The Rayleigh-Taylor instability is another classical test case for buoyancy-driven flows due to its practical and fundamental importance. It was investigated extensively in the literature by different numerical methods [73][74][75][76][77][78][79][80][81][82] . It consists of two layers of fluids of different densities (ρ H , ρ L ) at rest under gravitational field, as illustrated in Fig.…”

“…The investigated configuration was previously studied in the literature [73][74][75] with two target Reynolds numbers of 256 and 2048, The domain size is L x × 4L x , discretized with 256 × 1024 (fine mesh) or 128 × 512 grid points (coarse mesh). The heavy (index H) and light (index L) fluids are initially separated by a perturbed interface given by the following equation:…”