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Zhang S, Tang J, Wu H. Simplified wetting boundary scheme in phase-field lattice Boltzmann model for wetting phenomena on curved boundaries. Phys Rev E 2023; 108:025303. [PMID: 37723684 DOI: 10.1103/physreve.108.025303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 07/12/2023] [Indexed: 09/20/2023]
Abstract
In this work, a simplified wetting boundary scheme in the phase-field lattice Boltzmann model is developed for wetting phenomena on curved boundaries. The proposed scheme combines the advantages of the fluid-solid interaction scheme and geometric scheme-easy to implement (no need to interpolate the values of parameters exactly on solid boundaries and find proper characteristic vectors), the value of contact angle can be directly prescribed, and no unphysical spurious mass layer-and avoids mass leakage. Different from previous works, the values of the order parameter gradient on fluid boundary nodes are directly determined according to the geometric formulation rather than indirectly regulated through the order parameters on ghost solid nodes (i.e., ghost contact-line region). For this purpose, two numerical approaches to evaluate the order parameter gradient on fluid boundary nodes are utilized, one with the prevalent isotropic central scheme and the other with a local gradient scheme that utilizes the distribution functions. The simplified wetting boundary schemes with both numerical approaches are validated and compared through several numerical simulations. The results demonstrate that the proposed model has good ability and satisfactory accuracy to simulate wetting phenomena on curved boundaries under large density ratios.
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Affiliation(s)
- Shengyuan Zhang
- School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Jun Tang
- School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Huiying Wu
- School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China
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2
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Liu X, Chai Z, Shi B. Improved hybrid Allen-Cahn phase-field-based lattice Boltzmann method for incompressible two-phase flows. Phys Rev E 2023; 107:035308. [PMID: 37073063 DOI: 10.1103/physreve.107.035308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 03/16/2023] [Indexed: 04/20/2023]
Abstract
In this work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation (ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersion and eliminate the coarsening phenomenon. Then two LB models are adopted to solve the hybrid ACE and the Navier-Stokes equations, respectively. Through the Chapman-Enskog analysis, the present LB model can correctly recover the hybrid ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LB method is validated by five tests, including the diagonal translation of a circular interface, two stationary bubbles with different radii, a bubble rising under the gravity, the Rayleigh-Taylor instability in two-dimensional and three-dimensional cases, and the three-dimensional Plateau-Rayleigh instability. The numerical results show that the present LB method has a superior performance in reducing the numerical dispersion and the coarsening phenomenon.
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Affiliation(s)
- Xi Liu
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China; Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan, 430074, China; and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Zhenhua Chai
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China; Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan, 430074, China; and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Baochang Shi
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China; Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan, 430074, China; and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China
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Liang H, Wang R, Wei Y, Xu J. Lattice Boltzmann method for interface capturing. Phys Rev E 2023; 107:025302. [PMID: 36932607 DOI: 10.1103/physreve.107.025302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2022] [Accepted: 01/18/2023] [Indexed: 06/18/2023]
Abstract
Accurately solving phase interface plays a great role in modeling an immiscible multiphase flow system. In this paper, we propose an accurate interface-capturing lattice Boltzmann method from the perspective of the modified Allen-Cahn equation (ACE). The modified ACE is built based on the commonly used conservative formulation via the relation between the signed-distance function and the order parameter also maintaining the mass-conserved characteristic. A suitable forcing term is carefully incorporated into the lattice Boltzmann equation for correctly recovering the target equation. We then test the proposed method by simulating some typical interface-tracking problems of Zalesaks disk rotation, single vortex, deformation field and demonstrate that the present model can be more numerically accurate than the existing lattice Boltzmann models for the conservative ACE, especially at a small interface-thickness scale.
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Affiliation(s)
- Hong Liang
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Runlong Wang
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Yikun Wei
- Key Laboratory of Fluid Transmission Technology of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou 310018, China
| | - Jiangrong Xu
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
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Zhang C, Liang H, Guo Z, Wang LP. Discrete unified gas-kinetic scheme for the conservative Allen-Cahn equation. Phys Rev E 2022; 105:045317. [PMID: 35590655 DOI: 10.1103/physreve.105.045317] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 04/07/2022] [Indexed: 06/15/2023]
Abstract
In this paper, two discrete unified gas-kinetic scheme (DUGKS) methods with piecewise-parabolic flux reconstruction are presented for the conservative Allen-Cahn equation (CACE). One includes a temporal derivative of the order parameter in the force term while the other does not include temporal derivative in the force term but results in a modified CACE with additional terms. In the context of DUGKS, the continuum equations recovered from the piecewise-linear and piecewise-parabolic reconstructions for the fluxes at cell faces are subsequently derived. It is proved that the resulting equation with the piecewise-linear reconstruction is a first-order approximation to the discrete velocity kinetic equation due to the presence of the force term and the nonconservation property of the momentum of the collision model. To guarantee second-order accuracy of DUGKS, the piecewise-parabolic reconstruction for numerical flux is proposed. To validate the accuracy of the present DUGKS with the proposed flux evaluation, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zalesak disk and the deformation of a circular interface, have been simulated. Numerical results show that the accuracy of both proposed DUGKS methods is almost comparable and improved compared with the DUGKS with linear flux reconstruction scheme.
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Affiliation(s)
- Chunhua Zhang
- Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
| | - Hong Liang
- Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Zhaoli Guo
- State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Lian-Ping Wang
- Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
- Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
- Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
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An X, Dong B, Wang Y, Zhang Y, Zhou X, Li W. Coupled lattice Boltzmann-large eddy simulation model for three-dimensional multiphase flows at large density ratio and high Reynolds number. Phys Rev E 2021; 104:045305. [PMID: 34781498 DOI: 10.1103/physreve.104.045305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Accepted: 09/19/2021] [Indexed: 11/07/2022]
Abstract
A coupled lattice Boltzmann-large eddy simulation model is developed for modeling three-dimensional multiphase flows at large density ratios and high Reynolds numbers. In the framework of the lattice Boltzmann method, the model is proposed based on the standard Smagorinsky subgrid-scale approach, and a reconstructed multiple-relaxation-time collision operator is adopted. The conservative Allen-Cahn equation and Navier-Stokes equations are solved through the lattice Boltzmann discretization scheme for the interface tracking and velocity field evolution, respectively. Relevant benchmark cases are carried out to validate the performance of this model in simulating multiphase flows at a large density ratio and a high Reynolds number, including a stationary droplet, the process of spinodal decomposition, the Rayleigh-Taylor instability, the phenomenon of a droplet splashing on a thin liquid film, and the liquid jet breakup process. The maximum values of density ratio and Re number are 1000 and 10 240, respectively. The capability and reliability of the proposed model have been demonstrated by the good agreement between simulation results and the analytical solutions or the previously available results.
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Affiliation(s)
- Xiang An
- Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China
| | - Bo Dong
- Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China
| | - Yong Wang
- Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China
| | - Yajin Zhang
- Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China
| | - Xun Zhou
- Institute of Refrigeration and Air Conditioning Technology, Henan University of Science and Technology, Luoyang 471003, People's Republic of China
| | - Weizhong Li
- Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China
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Hosseini SA, Safari H, Thevenin D. Lattice Boltzmann Solver for Multiphase Flows: Application to High Weber and Reynolds Numbers. ENTROPY 2021; 23:e23020166. [PMID: 33573067 PMCID: PMC7911600 DOI: 10.3390/e23020166] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/26/2020] [Revised: 01/14/2021] [Accepted: 01/21/2021] [Indexed: 11/16/2022]
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.
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Affiliation(s)
- Seyed Ali Hosseini
- Laboratory of Fluid Dynamics and Technical Flows, University of Magdeburg “Otto von Guericke”, D-39106 Magdeburg, Germany; (H.S.); (D.T.)
- Department of Mechanical and Process Engineering, ETH Zürich, 8092 Zürich, Switzerland
- Correspondence:
| | - Hesameddin Safari
- Laboratory of Fluid Dynamics and Technical Flows, University of Magdeburg “Otto von Guericke”, D-39106 Magdeburg, Germany; (H.S.); (D.T.)
| | - Dominique Thevenin
- Laboratory of Fluid Dynamics and Technical Flows, University of Magdeburg “Otto von Guericke”, D-39106 Magdeburg, Germany; (H.S.); (D.T.)
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