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Kaushal S, Succi S, Ansumali S. Flow force calculation in the lattice Boltzmann method. Phys Rev E 2023; 108:045304. [PMID: 37978617 DOI: 10.1103/physreve.108.045304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Accepted: 08/17/2023] [Indexed: 11/19/2023]
Abstract
We revisit force evaluation methodologies on rigid solid particles suspended in a viscous fluid that is simulated via the lattice Boltzmann method (LBM). We point out the noncommutativity of streaming and collision operators in the force evaluation procedure due to the presence of a solid boundary, and provide a theoretical explanation for this observation. Based on this analysis, we propose a discrete force calculation scheme with enhanced accuracy. The proposed scheme is essentially a discrete version of the Reynolds transport theorem (RTT) in the context of a lattice Boltzmann formulation. Besides maintaining satisfactory levels of reliability and accuracy, the method also handles force evaluation on complex geometries in a simple and transparent way. We run benchmark simulations for flow past cylinder and NACA0012 airfoil (for Reynolds numbers ranging from 10^{2} to 0.5×10^{6}) and show that the current approach significantly reduces the grid size requirement for accurate force evaluation.
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Affiliation(s)
- Shaurya Kaushal
- Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
| | - Sauro Succi
- IIT@La Sapienza and Research Affiliate Physics Department Harvard University, Cambridge, Massachusetts 02138, USA
| | - Santosh Ansumali
- Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
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Liu Y, Yao Y, Li Q, Zhong X, He B, Wen B. Contact Angle Measurement on Curved Wetting Surfaces in Multiphase Lattice Boltzmann Method. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:2974-2984. [PMID: 36787627 DOI: 10.1021/acs.langmuir.2c02763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Contact angle is an essential physical quantity that characterizes the wettability of a substrate. Although it is widely used in the studies of surface wetting, capillary phenomena, and moving contact lines, the contact angle measurements in simulations and experiments are still complicated and time-consuming. In this paper, we present an efficient scheme for the measurement of contact angle on curved wetting surfaces in lattice Boltzmann simulations. The measuring results are in excellent agreement with the theoretical predictions without considering the gravity effect. A series of simulations with various drop sizes and surface curvatures confirm that the present scheme is grid-independent. Then, the scheme is verified in gravitational environments by simulating the deformations of sessile and pendent droplets on the curved wetting surface. The numerical results are highly consistent with experimental observations and support the theoretical analysis that the microscopic contact angle is independent of gravity. Furthermore, the method utilizes only the microscopic geometry of the contact angle and does not depend on the droplet profile; therefore, it can be applied to nonaxisymmetric shapes or moving contact lines. The scheme is applied to capture the dynamic contact angle hysteresis on homogeneous or chemically heterogeneous curved surfaces. Importantly, the accurate contact angle measurement enables the dynamic mechanical analysis of moving contact lines. The present measurement is simple and efficient and can be extended to implementations in various multiphase lattice Boltzmann models.
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Affiliation(s)
- Yangsha Liu
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Yichen Yao
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Quanying Li
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Xingguo Zhong
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Bing He
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Binghai Wen
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
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Wang F, Zhuang Z, Qin Z, Wen B. Movable and Focus-Tunable Lens Based on Electrically Controllable Liquid: A Lattice Boltzmann Study. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1714. [PMID: 36554119 PMCID: PMC9777668 DOI: 10.3390/e24121714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Revised: 11/13/2022] [Accepted: 11/21/2022] [Indexed: 06/17/2023]
Abstract
Adjusting the focal length by changing the liquid interface of the liquid lens has become a potential method. In this paper, the lattice-Boltzmann-electrodynamic (LB-ED) method is used to numerically investigate the zooming process of a movable and focus-tunable electrowetting-on-dielectrics (EWOD) liquid lens by combining the LBM chemical potential model and the electrodynamic model. The LB method is used to solve the Navier-Stokes equation, and the Poisson-Boltzmann (PB) equation is introduced to solve the electric field distribution. The experimental results are consistent with the theoretical results of the Lippmann-Young equation. Through the simulation of a liquid lens zoom driven by EWOD, it is found that the lens changes from a convex lens to a concave lens with the voltage increases. The focal length change rate in the convex lens stage gradually increases with voltage. In the concave lens stage, the focal length change rate is opposite to that in the convex lens stage. During the zooming process, the low-viscosity liquid exhibits oscillation, and the high-viscosity liquid appears as overdamping. Additionally, methods were proposed to accelerate lens stabilization at low and high viscosities, achieving speed improvements of about 30% and 50%, respectively. Simulations of lens motion at different viscosities demonstrate that higher-viscosity liquids require higher voltages to achieve the same movement speed.
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Affiliation(s)
- Fei Wang
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Zijian Zhuang
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Zhangrong Qin
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Binghai Wen
- Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
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Yao Y, Liu Y, Zhong X, Wen B. Multiphase curved boundary condition in lattice Boltzmann method. Phys Rev E 2022; 106:015307. [PMID: 35974580 DOI: 10.1103/physreve.106.015307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
The boundary treatment is fundamental for modeling fluid flows especially in the lattice Boltzmann method; the curved boundary conditions effectively improve the accuracy of single-phase simulations with complex-geometry boundaries. However, the conventional curved boundary conditions usually cause dramatic mass leakage or increase when they are directly used for multiphase flow simulations. We find that the principal reason for this is the absence of a nonideal effect in the curved boundary conditions, followed by a calculation error. In this paper, incorporating the nonideal effect into the linear interpolation scheme and compensating for the interpolating error, we propose a multiphase curved boundary condition to treat the wetting boundaries with complex geometries. A series of static and dynamic multiphase simulations with large density ratio verify that the present scheme is accurate and ensures mass conservation.
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Affiliation(s)
- Yichen Yao
- Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin 541004, China and School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Yangsha Liu
- Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin 541004, China and School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Xingguo Zhong
- Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin 541004, China and School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
| | - Binghai Wen
- Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin 541004, China and School of Computer Science and Engineering, Guangxi Normal University, Guilin 541004, China
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Numerical simulation of filtration processes in the flow-induced deformation of fibrous porous media by a three-dimensional two-way fluid–structure interaction scheme. Chem Eng Sci 2022. [DOI: 10.1016/j.ces.2022.117500] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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6
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DEM-LBM simulation of multidimensional fractionation by size and density through deterministic lateral displacement at various Reynolds numbers. POWDER TECHNOL 2021. [DOI: 10.1016/j.powtec.2021.02.062] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Comparison of numerical schemes for 3D lattice Boltzmann simulations of moving rigid particles in thermal fluid flows. POWDER TECHNOL 2019. [DOI: 10.1016/j.powtec.2019.07.054] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Ma Q, Chen Z, Liu H. Multiple-relaxation-time lattice Boltzmann simulation for flow, mass transfer, and adsorption in porous media. Phys Rev E 2018; 96:013313. [PMID: 29347115 DOI: 10.1103/physreve.96.013313] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2016] [Indexed: 11/07/2022]
Abstract
In this paper, to predict the dynamics behaviors of flow and mass transfer with adsorption phenomena in porous media at the representative elementary volume (REV) scale, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for the convection-diffusion equation is developed to solve the transfer problem with an unsteady source term in porous media. Utilizing the Chapman-Enskog analysis, the modified MRT-LB model can recover the macroscopic governing equations at the REV scale. The coupled MRT-LB model for momentum and mass transfer is validated by comparing with the finite-difference method and the analytical solution. Moreover, using the MRT-LB method coupled with the linear driving force model, the fluid transfer and adsorption behaviors of the carbon dioxide in a porous fixed bed are explored. The breakthrough curve of adsorption from MRT-LB simulation is compared with the experimental data and the finite-element solution, and the transient concentration distributions of the carbon dioxide along the porous fixed bed are elaborated upon in detail. In addition, the MRT-LB simulation results show that the appearance time of the breakthrough point in the breakthrough curve is advanced as the mass transfer resistance in the linear driving force model increases; however, the saturation point is prolonged inversely.
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Affiliation(s)
- Qiang Ma
- Institute for Energy Research, Jiangsu University, 301 Xuefu Road, Zhenjiang 212013, People's Republic of China.,Faculty of Engineering, University of Nottingham, University Park, Nottingham NG72RD, United Kingdom.,Jiangsu Provincial Key Laboratory of Solar Energy Science and Technology, School of Energy and Environment, Nanjing 210096, People's Republic of China
| | - Zhenqian Chen
- Jiangsu Provincial Key Laboratory of Solar Energy Science and Technology, School of Energy and Environment, Nanjing 210096, People's Republic of China
| | - Hao Liu
- Faculty of Engineering, University of Nottingham, University Park, Nottingham NG72RD, United Kingdom
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Dorschner B, Chikatamarla SS, Karlin IV. Entropic multirelaxation-time lattice Boltzmann method for moving and deforming geometries in three dimensions. Phys Rev E 2017; 95:063306. [PMID: 28709335 DOI: 10.1103/physreve.95.063306] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2017] [Indexed: 06/07/2023]
Abstract
Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work [B. Dorschner, S. Chikatamarla, F. Bösch, and I. Karlin, J. Comput. Phys. 295, 340 (2015)JCTPAH0021-999110.1016/j.jcp.2015.04.017] as well as for three-dimensional one-way coupled simulations of engine-type geometries in B. Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, and I. Karlin [J. Fluid Mech. 801, 623 (2016)JFLSA70022-112010.1017/jfm.2016.448] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases, including two-way coupling between fluid and structure and then turbulence and deforming geometries. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil in the transitional regime at a Reynolds number of Re=40000 and, finally, to access the model's performance for deforming geometries, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.
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Affiliation(s)
- B Dorschner
- Aerothermochemistry and Combustion Systems Lab, Department of Mechanical and Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland
| | - S S Chikatamarla
- Aerothermochemistry and Combustion Systems Lab, Department of Mechanical and Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland
| | - I V Karlin
- Aerothermochemistry and Combustion Systems Lab, Department of Mechanical and Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland
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Wen B, Zhou X, He B, Zhang C, Fang H. Chemical-potential-based lattice Boltzmann method for nonideal fluids. Phys Rev E 2017; 95:063305. [PMID: 28709336 DOI: 10.1103/physreve.95.063305] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2017] [Indexed: 06/07/2023]
Abstract
Chemical potential, as an important thermodynamic quantity, has been popularly used in thermodynamic modeling for complex systems, especially for those involving the phase transitions and chemical reactions. Here we present a chemical-potential-based multiphase lattice Boltzmann model, in which the nonideal force is directly evaluated by a chemical potential. The numerical computation is more efficient than the pressure-tensor-based model [Wen et al. Europhys. Lett. 112, 44002 (2015)10.1209/0295-5075/112/44002] because the calculations of the pressure tensor and its divergence are avoided. We have derived several chemical potentials of the popular equations of state from the free-energy density function. The theoretical analyses and numerical results support that the present model satisfies thermodynamics and Galilean invariance. An effective chemical-potential boundary condition is also implemented to investigate the wettability of a solid surface, and the contact angle can be linearly tuned by the surface chemical potential.
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Affiliation(s)
- Binghai Wen
- Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
- Division of Interfacial Water and Key Laboratory of Interfacial Physics and Technology, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China
| | - Xuan Zhou
- Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
| | - Bing He
- Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
| | - Chaoying Zhang
- Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
| | - Haiping Fang
- Division of Interfacial Water and Key Laboratory of Interfacial Physics and Technology, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China
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Peng C, Geneva N, Guo Z, Wang LP. Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method. Phys Rev E 2017; 95:013301. [PMID: 28208327 DOI: 10.1103/physreve.95.013301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2016] [Indexed: 06/06/2023]
Abstract
In lattice Boltzmann simulations involving moving solid boundaries, the momentum exchange between the solid and fluid phases was recently found to be not fully consistent with the principle of local Galilean invariance (GI) when the bounce-back schemes (BBS) and the momentum exchange method (MEM) are used. In the past, this inconsistency was resolved by introducing modified MEM schemes so that the overall moving-boundary algorithm could be more consistent with GI. However, in this paper we argue that the true origin of this violation of Galilean invariance (VGI) in the presence of a moving solid-fluid interface is due to the BBS itself, as the VGI error not only exists in the hydrodynamic force acting on the solid phase, but also in the boundary force exerted on the fluid phase, according to Newton's Third Law. The latter, however, has so far gone unnoticed in previously proposed modified MEM schemes. Based on this argument, we conclude that the previous modifications to the momentum exchange method are incomplete solutions to the VGI error in the lattice Boltzmann method (LBM). An implicit remedy to the VGI error in the LBM and its limitation is then revealed. To address the VGI error for a case when this implicit remedy does not exist, a bounce-back scheme based on coordinate transformation is proposed. Numerical tests in both laminar and turbulent flows show that the proposed scheme can effectively eliminate the errors associated with the usual bounce-back implementations on a no-slip solid boundary, and it can maintain an accurate momentum exchange calculation with minimal computational overhead.
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Affiliation(s)
- Cheng Peng
- Department of Mechanical Engineering, University of Delaware, Newark, Delaware 19716-3140, USA
| | - Nicholas Geneva
- Department of Mechanical Engineering, University of Delaware, Newark, Delaware 19716-3140, USA
| | - Zhaoli Guo
- State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, People's Republic of China
| | - Lian-Ping Wang
- Department of Mechanical Engineering, University of Delaware, Newark, Delaware 19716-3140, USA
- State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, People's Republic of China
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