We present high resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a Lattice Boltzmann method. We first validate the thermodynamical and kinematical properties of the algorithm. Then, we perform a series of 3d numerical simulations at changing the mean properties in the phase diagram and compare convection with and without phase coexistence at $Ra \sim 10^7$. We show that in presence of nucleating bubbles non-Oberbeck Boussinesq effects develops, mean temperature profile becomes asymmetric, heat-transfer and heat-transfer fluctuations are enhanced. We also show that small-scale properties of velocity and temperature fields are strongly affected by the presence of buoyant bubble leading to high non-Gaussian profiles in the bulk.
We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid-gas density ratios up to $10^3$. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation equations. We validate the model by showing that a stationary droplet obeys the Young-Laplace law, comparing the second oscillation mode of a droplet with respect to an analytical solution and showing correct mass conservation of a propagating density wave.
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 is the absence of nonideal effect in the curved boundary conditions, followed by the calculation error. In this paper, incorporating the nonideal effect into the linear …
The free energy model can extend the Lattice Boltzmann method to multiphase systems. However, there is a lack of models capable of simulating multicomponent multiphase fluids with partial miscibility. In addition, existing models cannot be generalized to honor thermodynamic information provided by any multicomponent equation of state of choice. In this paper, we introduce a free energy Lattice Boltzmann model where the forcing term is determined by the fugacity of the species, the thermodynamic property that connects species partial pressure to chemical potential calculations. By doing so, we …
A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [ Phys. Rev. E 47 1815 (1993)] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equations is demonstrated analytically by means of a Chapmann-Enskog expansion and numerically through several test cases. In particular, the model is benchmarked for its accuracy in reproducing the dynamics…
Current multi-component, multiphase pseudo-potential lattice Boltzmann models have thermodynamic inconsistencies that prevent them to correctly predict the thermodynamic phase behavior of partially miscible multi-component mixtures, such as hydrocarbon mixtures. This paper identifies these inconsistencies and attempts to design a thermodynamically consistent multi-component, multiphase pseudo-potential lattice Boltzmann model that allows mass transfer across the phase interfaces and is capable to predict the phase behavior of typically partially miscible hydrocarbon mixtures. The designed mode…
We present a lattice Boltzmann model for charged leaky dielectric multiphase fluids in the context of electrified jet simulations, which are of interest for a number of production technologies including electrospinning. The role of non-linear rheology on the dynamics of electrified jets is considered by exploiting the Carreau model for pseudoplastic fluids. We report exploratory simulations of charged droplets at rest and under a constant electric field, and we provide results for charged jet formation under electrospinning conditions.
A novel lattice Boltzmann (LB) model for multiphase flows is developed that complies with the thermodynamic foundations of kinetic theory. By directly devising the collision term for LB equation at the discrete level, a self-tuning equation of state is achieved, which can be interpreted as the incorporation of short-range molecular interaction. A pairwise interaction force is introduced to mimic the long-range molecular interaction, which is responsible for interfacial dynamics. The derived pressure tensor is naturally consistent with thermodynamic theory, and surface tension and interface thi…
In this paper, a lattice Boltzmann (LB) model is presented for axisymmetric multiphase flows. Source terms are added to a two-dimensional standard lattice Boltzmann equation (LBE) for multiphase flows such that the emergent dynamics can be transformed into the axisymmetric cylindrical coordinate system. The source terms are temporally and spatially dependent and represent the axisymmetric contribution of the order parameter of fluid phases and inertial, viscous and surface tension forces. A model which is effectively explicit and second order is obtained. This is achieved by taking into accoun…
In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the Chapman-Enskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corr…
Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly r…
The spurious currents observed in multiphase flow simulations with pseudo-potential lattice Boltzmann (LB) models are usually understood to be the result of the lack of isotropy of the model-generated interaction force between phases. Remedies have been proposed to utilize larger stencils to compute the interaction force with higher orders of isotropy. In this short communication, we point out the incompleteness in the current understanding and propose a new consistent implementation to more effectively suppress the spurious currents. We also demonstrate theoretically that certain low-level sp…
Shan-Chen model is a numerical scheme to simulate multiphase fluid flows using Lattice Boltzmann approach. The original Shan-Chen model suffers from inability to accurately predict behavior of air bubbles interacting in a non-aqueous fluid. In the present study, we extended the Shan-Chen model to take the effect of the attraction-repulsion barriers among bubbles in to account. The proposed model corrects the interaction and coalescence criterion of the original Shan-Chen scheme in order to have a more accurate simulation of bubbles morphology in a metal foam. The model is based on forming a th…
The aerosol formation is associated with the rupture of the liquid plug during the pulmonary airway reopening. The fluid dynamics of this process is difficult to predict because the rupture involved complex liquid-gas transition. Equation of state (EOS) plays a key role in the thermodynamic process of liquid-gas transition. Here, we propose an EOS-based multiphase lattice Boltzmann model, in which the nonideal force is directly evaluated by EOSs. This multiphase model is used to model the pulmonary airway reopening and study aerosol formation during exhalation. The numerical model is first val…
New method to simulate heat transport in multiphase lattice Boltzmann (LB) method is proposed. The energy transport equation needs to be solved when phase boundaries are present. Internal energy is represented by an additional set of distribution functions, which evolve according to a LB-like equation simulating the transport of a passive scalar. Parasitic heat diffusion near boundaries with large density gradient is supressed by using the interparticle "pseudoforces" which prevent the spreading of energy. The compression work and heat diffusion are calculated by finite differences. The latent…
Adaptive near-contact repulsion in conservative Allen-Cahn phase-field lattice Boltzmann multiphase model
Roma Tre University（罗马第三大学）；Pontifícia Universidade Católica do Paraná（巴拉那天主教大学）；Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche（意大利国家研究委员会计算应用研究所）；Center for Life Nano- & Neuro-Science, Fondazione Istituto Italiano di Tecnologia（意大利理工大学基金会生命纳米与神经科学中心）；PoreLab, Department of Physics, Norwegian University of Science and Technology（挪威科技大学物理系孔隙实验室）
The pseudo-potential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudo-potential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudo-potential LB model. Firstly, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme and the exact-difference-method (ED…
A high-performance implementation of a multiphase lattice Boltzmann method based on the conservative Allen-Cahn model supporting high-density ratios and high Reynolds numbers is presented. Metaprogramming techniques are used to generate optimized code for CPUs and GPUs automatically. The coupled model is specified in a high-level symbolic description and optimized through automatic transformations. The memory footprint of the resulting algorithm is reduced through the fusion of compute kernels. A roofline analysis demonstrates the excellent efficiency of the generated code on a single GPU. The…
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, measuring contact angles in experiments and simulations is still complicated and time-consuming. In this paper, we present an efficient scheme for the real-time and on-the-spot measurement of contact angles on curved wetting surfaces in lattice Boltzmann simulations. The measuring results are in excellent agreement with the theoretical predictions by the spherical cap method without conside…
It is shown that the Shan-Chen (SC) model for non-ideal lattice fluids can be made compliant with a pseudo free-energy principle by simple addition of a gradient force, whose expression is uniquely specified in terms of the fluid density. This additional term is numerically shown to provide fairly negligible effects on the system evolution during phase-separation. To the best of our knowledge, these important properties of the SC model were not noted before. The approach developed in the present work is based on a continuum analysis: further extensions, more in line with a discrete lattice the…
Convection heat transfer in porous media is a universal phenomenon in nature, and it is also frequently encountered in scientific and engineering fields. An in-depth understanding of the fundamental mechanism of convection heat transfer in porous media requires efficient and powerful numerical tools. In this paper, a cascaded lattice Boltzmann (CLB) method for convection heat transfer in porous media at the representative elementary volume (REV) scale is presented. In the CLB method, the flow field is solved by an isothermal CLB model with the D2Q9 lattice based on the generalized non-Darcy mo…
In this paper, an efficient three-dimensional lattice Boltzmann (LB) model with multiple-relaxation-time (MRT) collision operator is developed for the simulation of multiphase flows. This model is an extension of our previous two-dimensional model (H. Liang, B. C. Shi, Z. L. Guo, and Z. H. Chai, Phys. Rev. E. 89, 053320 (2014)) to the three dimensions using the D3Q7 (seven discrete velocities in three dimensions) lattice for the Chan-Hilliard equation (CHE) and the D3Q15 lattice for the Navier-Stokes equations (NSEs). Due to the smaller lattice-velocity numbers used, the computional efficiency…
In this paper, a double multiple-relaxation-time lattice Boltzmann model is developed for simulating transient solid-liquid phase change problems in porous media at the representative elementary volume scale. The model uses two different multiple-relaxation-time lattice Boltzmann equations, one for the flow field and the other for the temperature field with nonlinear latent heat source term. The model is based on the generalized non-Darcy formulation, and the solid-liquid phase change interface is traced through the liquid fraction which is determined by the enthalpy method. The model is valid…
Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Li et al., Phys. Rev. E. 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, thro…
A discrete Boltzmann model (DBM) is developed to investigate the hydrodynamic and thermodynamic non-equilibrium (TNE) effects in phase separation processes. The interparticle force drives changes and the gradient force, induced by gradients of macroscopic quantities, opposes them. In this paper, we investigate the interplay between them by providing detailed inspection of various non-equilibrium observables. Based on the TNE features, we define a TNE strength which roughly estimates the deviation amplitude from the thermodynamic equilibrium. The time evolution of the TNE intensity provides a c…
Double-diffusive convection in porous media is a common phenomenon in nature, and has received considerable attention in a wide variety of engineering applications. In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating double-diffusive convection in porous media at the representative elementary volume scale. The MRT-LB model is constructed in the framework of the triple-distribution-function approach: the velocity field, the temperature and concentration fields are solved separately by three different MRT-LB equations. The present model has tw…
The aim of this paper is twofold: the first is to formulate and validate a multi-scale discrete Boltzmann method (DBM) based on density functional kinetic theory for thermal multiphase flow systems, ranging from continuum to transition flow regime; the second is to present some new insights into the thermo-hydrodynamic non-equilibrium (THNE) effects in the phase separation process. Methodologically, DBM includes three main pillars: (i) the determination of the fewest kinetic moment relations, which are required by the description of significant THNE effects beyond the realm of continuum fluid …
In this paper, we aim to address an important issue about the pseudopotential lattice Boltzmann (LB) model, which has attracted much attention as a mesoscopic model for simulating interfacial dynamics of complex fluids, but suffers from the problem that the surface tension cannot be tuned independently of the density ratio. In the literature, a multi-range potential was devised to adjust the surface tension [Sbragaglia et al., Phys. Rev. E 75, 026702 (2007)]. However, it was recently found that the density ratio of the system will be changed when the multi-range potential is employed to adjust…
We present a novel approach to kinetic theory modeling enabling the simulation of a generic, real gas presented by its corresponding equation of state. The model is based on mass, momentum and energy conservation, and unlike the lattice Boltzmann models enables simulations of fluids exhibiting a liquid-vapor phase transition in both super- and subcritical states. In this new kinetic theory,an arbitrary equation of state can be introduced through rescaling the discrete particle velocities.Different benchmarks associated with real-gas thermodynamics illustrate that the proposed scheme can handle…
In this paper, a multiple-distribution-function lattice Boltzmann method (MDF-LBM) with multiple-relaxation-time model is proposed for incompressible Navier-Stokes equations (NSEs) which are considered as the coupled convection-diffusion equations (CDEs). Through direct Taylor expansion analysis, we show that the Navier-Stokes equations can be recovered correctly from the present MDF-LBM, and additionally, it is also found that the velocity and pressure can be directly computed through the zero and first-order moments of distribution function. Then in the framework of present MDF-LBM, we devel…
In the present work, the Tensor-Train decomposition algorithm is applied to reduce the memory footprint of a stochastic discrete velocity solver for rarefied gas dynamics simulation. An energy-conserving modification to the algorithm is proposed, along with an interleaved collision/convection routine which allows for easy application of higher-order convection schemes. The performance of the developed algorithm is analyzed for several 0- and 1-dimensional model problems in terms of solution error and reduction in memory use requirements.
In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for convection heat transfer in porous media under local thermal non-equilibrium (LTNE) condition. The model is constructed within the framework of the three-distribution-function approach: two temperature-based MRT-LB equations are proposed for the temperature fields of fluid and solid phases in addition to the MRT-LB equation of a density distribution function for the velocity field described by the generalized non-Darcy model. The thermal non-equilibrium effects are incorporated into the model by adding…
We present a novel lattice Boltzmann method that has a capability of simulating thermodynamic multiphase flows. This approach is fully thermodynamically consistent at the macroscopic level. Using this new method, a liquid-vapor boiling process, including liquid-vapor formation and coalescence together with a full coupling of temperature, is simulated for the first time.
Simulation of multiphase flows require coupled capturing or tracking of the interfaces in conjunction with the solution of fluid motion often occurring at multiple scales. We will present unified cascaded LB methods based on central moments for the solution of the incompressible two-phase flows at high density ratios and for capturing of the interfacial dynamics. Based on a modified continuous Boltzmann equation (MCBE) for two-phase flows, where a kinetic transformation to the distribution function involving the pressure field is introduced to reduce the associated numerical stiffness at high …
The Lattice Boltzmann method has been gaining acceptance for hydrodynamic problems involving complex boundaries, non-equilibrium dynamics and interfacial phenomena in multiphase or multicomponent systems. lb2d.pm is a Perl module offering a clear framework for simple Lattice Boltzmann simulations in 2D. The syntax and some basic applications are presented. Mainly, the new version 0.1 enables solute transport and accounts for reactive boundaries leading to surface growth.
When boiling occurs in a liquid flow field, the phenomenon is known as forced-convection boiling. We numerically investigate such a boiling system on a cylinder in a flow at a saturated condition. To deal with the complicated liquid-vapor phase-change phenomenon, we develop a numerical scheme based on the pseudopotential lattice Boltzmann method (LBM). The collision stage is performed in the space of central moments (CMs) to enhance numerical stability for high Reynolds numbers. The adopted forcing scheme, consistent with the CMs-based LBM, leads to a concise yet robust algorithm. Furthermore,…
We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function approach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal co…
Self-rewetting fluids (SRFs), such as aqueous solutions of long-chain alcohols, exhibit anomalous quadratic dependence of surface tension on temperature having a minimum and with a positive gradient. When compared to the normal fluids (NFs), the SRFs can be associated with significantly modified interfacial dynamics, which have recently been exploited to enhance flow and thermal transport in various applications (e.g., microgravity and microscale transport systems). In this work, first, we develop a new analytical solution of thermocapillary convection in superimposed two SRF layers confined w…
The pseudopotential multiphase lattice Boltzmann (LB) model is a very popular model in the LB community for simulating multiphase flows. When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary. In this work, we aim at investigating the implementation of contact angles in the pseudopotential LB simulations with curved boundaries. In the pseudopotential LB model, the contact angle is usually realized by employing a solid-fluid interaction or specifying a constant virtual wall density. However, it is shown that the…
We propose a novel fluid-structure interaction (FSI) scheme using the entropic multi-relaxation time lattice Boltzmann (KBC) model for the fluid domain in combination with a nonlinear finite element solver for the structural part. We show validity of the proposed scheme for various challenging set-ups by comparison to literature data. Beyond validation, we extend the KBC model to multiphase flows and couple it with FEM solver. Robustness and viability of the entropic multi-relaxation time model for complex FSI applications is shown by simulations of droplet impact on elastic superhydrophobic s…
We present the Fluid Transport Accelerated Solver, FluTAS, a scalable GPU code for multiphase flows with thermal effects. The code solves the incompressible Navier-Stokes equation for two-fluid systems, with a direct FFT-based Poisson solver for the pressure equation. The interface between the two fluids is represented with the Volume of Fluid (VoF) method, which is mass conserving and well suited for complex flows thanks to its capacity of handling topological changes. The energy equation is explicitly solved and coupled with the momentum equation through the Boussinesq approximation. The cod…
The fluid dynamics video presented here outlines recent advances in the simulation of multiphase cellular blood flow through the direct numerical simulations of deformable red blood cells (RBCs) demonstrated through several numerical experiments. Videos show RBC deformations in variety of numerical simulations, relative viscosity of a suspension of RBCs in shear, and the cell-depleted wall layer for blood Hagen--Poiseuille flow.
In the present study, two schemes named face discernment and flux correction are proposed to achieve single-phase transportation of free charge in multiphase electrohydrodynamic(EHD) problems. Many EHD phenomena occur between air and another liquid while the free charge can only be transported in the liquid phase through ohmic conduction and convection due to the poor conductivity of air. However, the charge may be leaked into the dielectric air during the simulation due to the asynchronous transportation between interface and free charge. To avoid this unphysical error, a face discernment met…
