An interfacial lattice Boltzmann flux solver for simulation of multiphase flows at large density ratio

Lan-shao, You; Niu, Xiaodong; Wang, Yan; Khan, Adnan; Li, Qiao-Zhong

doi:10.1016/j.ijmultiphaseflow.2019.04.006

Cited by 22 publications

(25 citation statements)

References 48 publications

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“…e multiple-relaxation-time collision operator is applied to study the influence of different parameters, including the gas/liquid viscosity ratio and liquid film thickness. Wang et al [24] and Li et al [25] have built an interfacial lattice Boltzmann flux solver for high-density ratio multiphase phenomena, and the droplet splashing on the stationary thin film is also simulated successfully. Due to the existence of the shear stress in the liquid film, the dynamic behaviors of the droplet impact on a moving liquid film are more complex.…”

Section: Introductionmentioning

confidence: 99%

Droplet Impact on a Moving Thin Film with Pseudopotential Lattice Boltzmann Method

Yuan

et al. 2020

Mathematical Problems in Engineering

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The pseudopotential lattice Boltzmann method (LBM) with a tunable surface tension term is applied to study a droplet impact on a moving thin film. The Re effects of dimensionless parameters on the upstream and downstream crown evolution are studied, including Reynolds number (Re), Weber number (We), liquid film thickness, and horizontal velocity of the liquid film. The movement of the liquid film causes the asymmetry development of the upstream and downstream crown. Both the instability of upstream and downstream crowns increases with the increase of Re and We, and the upstream crown becomes more prone to break up. And a critical value of film thickness exists with the height of the upstream and downstream liquid crowns reaches the maximum value. And the velocity of liquid film restrains the development of the height of the upstream and downstream crowns, but it promotes the growth of the crown radius.

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Section: Introductionmentioning

confidence: 99%

Droplet Impact on a Moving Thin Film with Pseudopotential Lattice Boltzmann Method

Yuan

et al. 2020

Mathematical Problems in Engineering

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“…The LB evolution equation with the BGK collision operator for C‐H equation can be written as 26,31,34 :

g_{α} false(x + {bold-italice}_{α} Δ t, t + Δ t false) - g_{α} false(x, t false) = \frac{g_{α}^{italiceq} false(x, t false) - g_{α} false(x, t false)}{τ_{g}} + Δ {italictG}_{α} false(x, t false), α = 0, 1, \dots, N,

where g α is the distribution function for order parameter with discrete velocity e α at physical location x = ( x , y ) and time step t ; τ g is the non‐dimensional relaxation parameter related to the mobility; N is the number of the streaming directions, and the superscript eq of g α denotes a local equilibrium state which is given by 20,30,35 :

g_{α}^{italiceq} = \{\begin{matrix} left \\ ϕ - 3 μ_{ϕ} θ_{M} false(1 - ω_{α} false) α = 0, \\ 3 ω_{α} false(μ_{ϕ} θ_{M} + ϕ {bold-italice}_{α} \cdot u false) α = 1, \dots, N, \end{matrix}

here ω α is the weighting coefficient which is given by ω 0 = 4/9, ω 1 − 4 = 1/9, ω 5 − 8 = 1/36 in D2Q9 model, and the discrete velocities can be defined as 36 :

{bold-italice}_{α} = \{\begin{matrix} left \\ false(0, 0 false) c, α = 0... \end{matrix}

…”

Section: Methodsologymentioning

confidence: 99%

“…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%

“…Similar to the work of Shao et al, 19 the stable high‐order WENO difference scheme was utilized to solve C‐H equation. In the latest study of Li et al, 20 they introduced an interfacial LB flux solver, in which both C‐H equation and N‐S equations were solved by the cell‐centered finite volume method. The numerical tests indicated good performance in capturing complex interfacial changes and conserving the mass balance.…”

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 simplified lattice Boltzmann flux solver for multiphase flows with large density ratio

Yang

Chen

Жен

et al. 2021

Numerical Methods in Fluids

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Unlike the conventional multiphase lattice Boltzmann method (LBM), the recently developed finite volume‐based multiphase lattice Boltzmann flux solver (MLBFS) is free from the limitation of the uniform mesh, the coupled time step and mesh spacing, and the high virtual memories. In the MLBFS, the macroscopic equations recovered from the LBM are discretized by the finite volume method while the fluxes at the cell interfaces are evaluated based on the local application of LBM. The interfacial fluxes are calculated only by the distribution functions. However, the code implementation involving too many distribution functions is still not simple enough. And the computation of the distribution functions will still cost relatively large computational resources. We notice that some moments of the distribution functions can be directly simplified as the macroscopic variables. Therefore, to further simplify the code implementation and improve the computational efficiency of the MLBFS, we propose a simplified MLBFS which reconstructs the fluxes with the combination of the distribution functions and the macroscopic variables. Naturally, we can expect that the simplified method can improve the computational efficiency while maintaining the numerical accuracy and reliability of the original MLBFS. Numerical experiments of the Laplace law, the Rayleigh–Taylor instability, the bubble rising under buoyancy and the droplet splashing on a liquid film are conducted to evaluate the simplified MLBFS. Results show that our method can save up to 18.32% of the original computational time. The simplified method is superior to the original one especially for the cases with a large number of girds.

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An interfacial lattice Boltzmann flux solver for simulation of multiphase flows at large density ratio

Cited by 22 publications

References 48 publications

Droplet Impact on a Moving Thin Film with Pseudopotential Lattice Boltzmann Method

Droplet Impact on a Moving Thin Film with Pseudopotential Lattice Boltzmann Method

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

A simplified lattice Boltzmann flux solver for multiphase flows with large density ratio

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