A brief review of the phase-field-based lattice Boltzmann method for multiphase flows

Wang, Huili; Yuan, Xiaolei; Liang, Hong; Chai, Zhenhua; Shi, Baochang

doi:10.26804/capi.2019.03.01

Cited by 128 publications

(66 citation statements)

References 100 publications

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“…Nevertheless, it was observed to be very effective and robust for multiphase flows in the incompressible regime, and readily able to deal with larger Weber numbers. For a more comprehensive overview of the developments of such models, interested readers are referred to [ 18 ]. Approaches relying on the explicit tracking of the interface with a consistent energy functional making use of the nonideal EoS were also proposed as ways to improve the stability of the original free-energy formulation [ 19 , 20 ].…”

Section: Introductionmentioning

confidence: 99%

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

Hosseini

Safari

Thévenin

2021

Entropy

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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.

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Section: Introductionmentioning

confidence: 99%

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

Hosseini

Safari

Thévenin

2021

Entropy

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“…The pore network model [7][8][9] usually uses a simple geometry pore network, which is insufficient to solve the complex pore structure fluid flow. The lattice Boltzmann method [10][11][12][13][14] uses the discrete medium model to simulate fluid motion. Interface capture methods based on Navier-Stokes equations include the volume-of-fluid method (VOF), the level-set method (LSM), and the phase-field method (PFM).…”

Section: Introductionmentioning

confidence: 99%

Phase-Field Simulation of Imbibition for the Matrix-Fracture of Tight Oil Reservoirs Considering Temperature Change

Jin

Cheng

Cao

et al. 2021

Water

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Injection water temperature is often different from that of the reservoir during water injection development in the tight reservoir. Temperature change causes different fluid properties and oil-water interface properties, which further affects the imbibition process. In this paper, a matrix-fracture non-isothermal oil-water imbibition flow model in tight reservoirs is established and solved by the finite element method based on the phase-field method. The ideal inhomogeneous rock structure model was used to study the influence of a single factor on the imbibition. The actual rock structure model was used to study the influence of temperature. The mechanism of temperature influence in the process of imbibition is studied from the micro-level. It is found that the imbibition of matrix-fracture is a process in which the water enters the matrix along with the small pores, and the oil is driven into the macropores and then into the fractures. Temperature affects the imbibition process by changing the oil-water contact angle, oil-water interfacial tension, and oil-water viscosity ratio. Reducing oil-water contact angle and oil-water viscosity ratio and increasing oil-water interfacial tension are conducive to the imbibition process. The increase in injection water temperature is usually beneficial to the occurrence of the imbibition. Moreover, the actual core structure imbibition degree is often lower than that of the ideal core structure. The inhomogeneous distribution of rock particles has a significant influence on imbibition. This study provides microscale theoretical support for seeking reasonable injection velocity, pressure gradient, injection temperature, and well-shutting time in the field process. It provides a reference for the formulation of field process parameters.

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“…Thus, there are two different phase‐field based multiphase models: one is to couple C‐H equation with N‐S equations and another is to couple A‐C equation with N‐S equations. In the recent decade, interests are growing in adopting the phase‐field theory to simulate multiphase flows, among which the LBM has attracted wide publicity 13‐32 …”

Section: Introductionmentioning

confidence: 99%

“…In view of this, a very interesting work was presented by Hu et al, 28 in which a hybrid local and nonlocal A‐C equation based LB model was constructed for reducing the numerical dispersion. And a good review of previous phase‐field based LB models and some recent processes in the field can be found in Reference 29.…”

Section: Introductionmentioning

confidence: 99%

“…The above mentioned studies indicate that the successful improvement of multiphase LB models for problems with density ratio include: (a) the correction step for the pressure, 13,30,31 (b) the directional derivatives for the gradient terms, 14 and (c) the MRT collision operators 17,18,23 . Furthermore, most recent studies show that the solution of the phase‐field equation has a great influence on numerical stability for modeling multiphase problems with density ratios 18‐29,32 . As we know, realistic multiphase flows in nature belong to a density ratio regime of 1000, but there exist quite a few fields that involve a density ratio larger than 1000, especially in industrial applications.…”

Section: Introductionmentioning

confidence: 99%

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A high‐order phase‐field based lattice Boltzmann model for simulating complex multiphase flows with large density ratios

Zhou

et al. 2020

Numerical Methods in Fluids

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SummaryBased on phase‐field theory, we develop a simple and robust single relaxation time (SRT) lattice Boltzmann (LB) model for simulating complex multiphase flows with large density ratios (up to 2000). The approach utilizes two LB equations (LBE), one is used to describe the interface behavior and the other is used to calculate the hydrodynamic properties. To improve the accuracy and stability in capturing interface, the high‐order LB model derived through the fourth‐order Chapman‐Enskog expansion analysis is applied to Cahn‐Hilliard equation. For solution of the flow field, a modified particle distribution function in the pressure‐velocity formulation is constructed to correctly consider the effect of local density variation and continuous pressure field. With such improvement, the proposed multiphase LB model is able to maintain numerical stability for the problem with very large density ratio, lower relaxation parameter and complex interface. For validation, a series of benchmark cases are carried out. Specially, the full potential of the proposed model is validated by bubble bursting at a free surface, bubble rising and droplet splashing with a density ratio of 2000. In all test cases, the obtained numerical results agree well with the reference data or the analytical solutions.

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A brief review of the phase-field-based lattice Boltzmann method for multiphase flows

Cited by 128 publications

References 100 publications

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

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

Phase-Field Simulation of Imbibition for the Matrix-Fracture of Tight Oil Reservoirs Considering Temperature Change

A high‐order phase‐field based lattice Boltzmann model for simulating complex multiphase flows with large density ratios

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