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Saito S, Takada N, Baba S, Someya S, Ito H. Generalized equilibria for color-gradient lattice Boltzmann model based on higher-order Hermite polynomials: A simplified implementation with central moments. Phys Rev E 2023; 108:065305. [PMID: 38243429 DOI: 10.1103/physreve.108.065305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 11/19/2023] [Indexed: 01/21/2024]
Abstract
We propose generalized equilibria of a three-dimensional color-gradient lattice Boltzmann model for two-component two-phase flows using higher-order Hermite polynomials. Although the resulting equilibrium distribution function, which includes a sixth-order term on the velocity, is computationally cumbersome, its equilibrium central moments (CMs) are velocity-independent and have a simplified form. Numerical experiments show that our approach, as in Wen et al. [Phys. Rev. E 100, 023301 (2019)2470-004510.1103/PhysRevE.100.023301] who consider terms up to third order, improves the Galilean invariance compared to that of the conventional approach. Dynamic problems can be solved with high accuracy at a density ratio of 10; however, the accuracy is still limited to a density ratio of 1000. For lower density ratios, the generalized equilibria benefit from the CM-based multiple-relaxation-time model, especially at very high Reynolds numbers, significantly improving the numerical stability.
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Affiliation(s)
- Shimpei Saito
- Research Institute for Energy Conservation (iECO), National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba 3058564, Japan
| | - Naoki Takada
- Research Institute for Energy Conservation (iECO), National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba 3058564, Japan
| | - Soumei Baba
- Research Institute for Energy Conservation (iECO), National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba 3058564, Japan
| | - Satoshi Someya
- Research Institute for Energy Conservation (iECO), National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba 3058564, Japan
| | - Hiroshi Ito
- Research Institute for Energy Conservation (iECO), National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba 3058564, Japan
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2
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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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3
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Wang L, Huang J, He K. Thermal lattice Boltzmann model for liquid-vapor phase change. Phys Rev E 2022; 106:055308. [PMID: 36559346 DOI: 10.1103/physreve.106.055308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 10/27/2022] [Indexed: 06/17/2023]
Abstract
The lattice Boltzmann method is adopted to solve the liquid-vapor phase change problems in this article. By modifying the collision term for the temperature evolution equation, a thermal lattice Boltzmann model is constructed. As compared with previous studies, the most striking feature of the present approach is that it could avoid the calculations of both the Laplacian term of temperature [∇·(κ∇T)] and the gradient term of heat capacitance [∇(ρc_{v})]. In addition, since the present approach adopts a simple linear equilibrium distribution function, it is possible to use the D2Q5 lattice for the two-dimensional cases considered here. Thus, the present model is more efficient than previous models in which the lattice is usually limited to the D2Q9. The proposed model is first validated by the problems of droplet evaporation in open space and droplet evaporation on a heated surface, and the numerical results show good agreement with the analytical results and the finite difference method. Then it is used to model the nucleate boiling problem, and the relationship between detachment bubble diameter and gravitational acceleration obtained with the present approach fits well with previous works.
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Affiliation(s)
- Lei Wang
- School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China and Center for Mathematical Sciences, China University of Geosciences, Wuhan 430074, China
| | - Jiangxu Huang
- School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China and Center for Mathematical Sciences, China University of Geosciences, Wuhan 430074, China
| | - Kun He
- School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China and Center for Mathematical Sciences, China University of Geosciences, Wuhan 430074, China
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Fei L, Qin F, Zhao J, Derome D, Carmeliet J. Pore-Scale Study on Convective Drying of Porous Media. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:6023-6035. [PMID: 35512019 DOI: 10.1021/acs.langmuir.2c00267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this work, a numerical model for isothermal liquid-vapor phase change (evaporation) of the two-component air-water system is proposed based on the pseudopotential lattice Boltzmann method. Through the Chapman-Enskog multiscale analysis, we show that the model can correctly recover the macroscopic governing equations of the multicomponent multiphase system with a built-in binary diffusion mechanism. The model is verified based on the two-component Stefan problem where the measured binary diffusivity is consistent with theoretical analysis. The model is then applied to convective drying of a dual-porosity porous medium at the pore scale. The simulation captures a classical transition in the drying process of porous media, from the constant rate period (CRP, first phase) showing significant capillary pumping from large to small pores, to the falling rate period (FRP, second phase) with the liquid front receding in small pores. It is found that, in the CRP, the evaporation rate increases with the inflow Reynolds number (Re), while in the FRP, the evaporation curves almost collapse at different Res. The underlying mechanism is elucidated by introducing an effective Péclet number (Pe). It is shown that convection is dominant in the CRP and diffusion in the FRP, as evidenced by Pe > 1 and Pe < 1, respectively. We also find a log-law dependence of the average evaporation rate on the inflow Re in the CRP regime. The present work provides new insights into the drying physics of porous media and its direct modeling at the pore scale.
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Affiliation(s)
- Linlin Fei
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8092, Switzerland
| | - Feifei Qin
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8092, Switzerland
| | - Jianlin Zhao
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8092, Switzerland
| | - Dominique Derome
- Department of Civil and Building Engineering, Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada
| | - Jan Carmeliet
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8092, Switzerland
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Wang G, Fei L, Luo KH. Unified lattice Boltzmann method with improved schemes for multiphase flow simulation: Application to droplet dynamics under realistic conditions. Phys Rev E 2022; 105:045314. [PMID: 35590633 DOI: 10.1103/physreve.105.045314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
As a powerful mesoscale approach, the lattice Boltzmann method (LBM) has been widely used for the numerical study of complex multiphase flows. Recently, Luo et al. [Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 379, 20200397 (2021)10.1098/rsta.2020.0397] proposed a unified lattice Boltzmann method (ULBM) to integrate the widely used lattice Boltzmann collision operators into a unified framework. In this study, we incorporate additional features into this ULBM in order to simulate multiphase flow under realistic conditions. A nonorthogonal moment set [Fei et al., Phys. Rev. E 97, 053309 (2018)10.1103/PhysRevE.97.053309] and the entropic-multi-relaxation-time (KBC) lattice Boltzmann model are used to construct the collision operator. An extended combined pseudopotential model is proposed to realize multiphase flow simulation at high-density ratio with tunable surface tension over a wide range. The numerical results indicate that the improved ULBM can significantly decrease the spurious velocities and adjust the surface tension without appreciably changing the density ratio. The ULBM is validated through reproducing various droplet dynamics experiments, such as binary droplet collision and droplet impingement on superhydrophobic surfaces. Finally, the extended ULBM is applied to complex droplet dynamics, including droplet pancake bouncing and droplet splashing. The maximum Weber number and Reynolds number in the simulation reach 800 and 7200, respectively, at a density ratio of 1000. The study demonstrates the generality and versatility of ULBM for incorporating schemes to tackle challenging multiphase problems.
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Affiliation(s)
- Geng Wang
- Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - Linlin Fei
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8092, Switzerland
| | - Kai H Luo
- Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
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Fei L, Qin F, Wang G, Luo KH, Derome D, Carmeliet J. Droplet evaporation in finite-size systems: Theoretical analysis and mesoscopic modeling. Phys Rev E 2022; 105:025101. [PMID: 35291136 DOI: 10.1103/physreve.105.025101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 01/17/2022] [Indexed: 06/14/2023]
Abstract
The classical D^{2}-Law states that the square of the droplet diameter decreases linearly with time during its evaporation process, i.e., D^{2}(t)=D_{0}^{2}-Kt, where D_{0} is the droplet initial diameter and K is the evaporation constant. Though the law has been widely verified by experiments, considerable deviations are observed in many cases. In this work, a revised theoretical analysis of the single droplet evaporation in finite-size open systems is presented for both two-dimensional (2D) and 3D cases. Our analysis shows that the classical D^{2}-Law is only applicable for 3D large systems (L≫D_{0}, L is the system size), while significant deviations occur for small (L≤5D_{0}) and/or 2D systems. Theoretical solution for the temperature field is also derived. Moreover, we discuss in detail the proper numerical implementation of droplet evaporation in finite-size open systems by the mesoscopic lattice Boltzmann method (LBM). Taking into consideration shrinkage effects and an adaptive pressure boundary condition, droplet evaporation in finite-size 2D/3D systems with density ratio up to 328 within a wide parameter range (K=[0.003,0.18] in lattice units) is simulated, and remarkable agreement with the theoretical solution is achieved, in contrast to previous simulations. The present work provides insights into realistic droplet evaporation phenomena and their numerical modeling using diffuse-interface methods.
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Affiliation(s)
- Linlin Fei
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8092, Switzerland
| | - Feifei Qin
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8092, Switzerland
| | - Geng Wang
- Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - Kai H Luo
- Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - Dominique Derome
- Department of Civil and Building Engineering, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
| | - Jan Carmeliet
- Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8092, Switzerland
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Czelusniak LE, Mapelli VP, Wagner AJ, Cabezas-Gómez L. Shaping the equation of state to improve numerical accuracy and stability of the pseudopotential lattice Boltzmann method. Phys Rev E 2022; 105:015303. [PMID: 35193246 DOI: 10.1103/physreve.105.015303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Accepted: 12/09/2021] [Indexed: 11/07/2022]
Abstract
It has recently been shown that altering the shape of the metastable and unstable branches of an equation of state (EOS) can substantially improve the numerical accuracy of liquid and vapor densities in the pseudopotential lattice Boltzmann method [Peng et al., Phys. Rev. E 101, 063309 (2020)2470-004510.1103/PhysRevE.101.063309]. We found that this approach reduces stability of the method in nonequilibrium conditions and is unstable for bubbles at low reduced temperatures. Here we present an improved method for altering the shape of the metastable and unstable branches of the EOS which remains stable for both equilibrium and nonequilibrium situations and has no issues with bubbles. We also performed a detailed study of the stability of the methods for a droplet impact on a liquid film for reduced temperatures down to 0.35 with Reynolds number of 300. Our approach remained stable for a density ratio of up to 3.38×10^{4}.
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Affiliation(s)
- Luiz Eduardo Czelusniak
- Department of Mechanical Engineering, Engineering School of São Carlos, University of São Paulo, São Carlos, São Paulo 13566-590, Brazil
| | - Vinícius Pessoa Mapelli
- Department of Mechanical Engineering, Engineering School of São Carlos, University of São Paulo, São Carlos, São Paulo 13566-590, Brazil
| | - Alexander J Wagner
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108, USA
| | - Luben Cabezas-Gómez
- Department of Mechanical Engineering, Engineering School of São Carlos, University of São Paulo, São Carlos, São Paulo 13566-590, Brazil
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Di Ilio G, Chiappini D, Falcucci G, Succi S. Progress in mesoscale methods for fluid dynamics simulation. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200393. [PMID: 34455837 DOI: 10.1098/rsta.2020.0393] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 07/07/2021] [Indexed: 06/13/2023]
Affiliation(s)
- Giovanni Di Ilio
- Department of Engineering, University of Naples 'Parthenope', Centro Direzionale, Isola C4, Naples 80143, Italy
| | - Daniele Chiappini
- Department of Engineering, University of Rome 'Niccolo Cusano', Via Don Carlo Gnocchi 3, Rome 00166, Italy
| | - Giacomo Falcucci
- Department of Enterprise Engineering 'Mario Lucertini', University of Rome 'Tor Vergata', Via del Politecnico 1, Rome 00133, Italy
- Department of Physics, Harvard University, 17 Oxford Street, 02138 Cambridge, MA, USA
| | - Sauro Succi
- Italian Institute of Technology, P.le Aldo Moro 1, Rome 00185, Italy
- Institute of Applied Computing - National Research Council of Italy, Via dei Taurini 19, Rome 00185, Italy
- Department of Physics, Harvard University, 17 Oxford Street, 02138 Cambridge, MA, USA
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