D2Q9 Model Research Articles

Surface wettability analysis using a microdroplet: a numerical approach

Analysis of hydrophobicity is essential for learning about the characteristics of molecules, surfaces, and materials that reject water. Using a two-dimensional (2D) pseudo-potential multiphase lattice Boltzmann approach with a D2Q9 model, this work examines the influence of solid-fluid interaction strength on wettability and hydrophobicity of smooth surfaces. To ascertain the contact angle and assess the accuracy of the numerical model, the study considers the equilibrium state of a water droplet on a smooth surface. In a 200×200 lattice unit domain, droplets having a radius of 60 lattice units are used to assess the hydrophobicity of smooth surfaces. According to the research, there is a large rise in the contact area between solid walls and water droplets when the solid-fluid interaction parameter is raised, which leads to a greater degree of hydrophobicity. By measuring the contact angle between the solid and fluid-vapor interface for different surfaces, it is observed that as G_ads becomes more negative, the contact angle decreases, indicating increased surface hydrophobicity, and the effect on droplet spreading is also highlighted in the research.

Quantifying surface wettability in textured surfaces using two-dimensional pseudo-potential multiphase lattice Boltzmann model

Surface wettability plays a critical role in microfluidic applications, enabling enhanced fluid flow control, minimizing sample waste, and improving efficiency across various fields, including drying technology, food processing, chemical manufacturing, and ­environmental engineering. This study presents a numerical investigation of surface wettability on textured surfaces utilizing a two-dimensional (2D) pseudo-potential multiphase lattice Boltzmann method (LBM) with a D2Q9 model. The analysis is conducted for a range of solid-fluid interaction parameters (Gads ), varying between −2.50 and −1.40. Initially, the equilibrium state of a water droplet on a flat surface is simulated for different interaction parameters to validate the accuracy of the numerical model. Subsequently, micropillars are introduced on the bottom wall of the surface with varying heights and spacings to create hydrophobic and superhydrophobic textures, resulting in enhanced contact angles. The wettability of these surfaces is analyzed by placing a water droplet with a radius of 30 lattice units at the center of a computational domain sized 200 × 200 lattice units. The findings reveal that increasing the interaction parameter on textured surfaces significantly reduces the contact area between the droplet and the solid surface due to the momentum redirection effect, thereby increasing surface surface wettability. Similarly, greater spacing between micropillars enhances surface surface wettability. The simulated contact angles for various interaction strengths have been qualitatively validated with previously reported results, confirming the robustness of the present numerical model.

The Dissipation of the Kinetic Energy for 2D Bounded Flow by Using Moment-Based Boundary Conditions with Burnett Order Stress for LBM

In this article, the lattice Boltzmann method with two relaxation time (TRT) for the D2Q9 model is used to investigate numerical results for 2D flow. The problem is performed to show the dissipation of the kinetic energy rate and its relationship with the enstrophy growth for 2D dipole wall collision. The investigation is carried out for normal collision and oblique incidents at an angle of . We prove the accuracy of moment -based boundary conditions with slip and Navier-Maxwell slip conditions to simulate this flow. These conditions are under the effect of Burnett-order stress conditions that are consistent with the discrete Boltzmann equation. Stable results are found by using this kind of boundary condition where dissipation of the kinetic energy is found to be proportional to in the first regime and it is in the second part of the regime as expected. An excellent agreement with the benchmark data is observed.

On Lattice Boltzmann Methods based on vector-kinetic models for hyperbolic partial differential equations

On Lattice Boltzmann Methods based on vector-kinetic models for hyperbolic partial differential equations

LBM modeling of three-dimensional mixed convection in CZ crystal growth on curvilinear coordinates system

LBM modeling of three-dimensional mixed convection in CZ crystal growth on curvilinear coordinates system

Distinctions of the Emergence of Convective Flows at the “Diffusion–Convections” Boundary in Isothermal Ternary Gas Mixtures with Carbon Dioxide

This study discusses the influence of the composition of a ternary gas mixture on the possibility of occurrence of convective instability under isothermal conditions due to the difference in the diffusion abilities of the components. A numerical study was carried out to study the change in “diffusion–concentration gravitational convection” modes in an isothermal three-component gas mixture He + CO2 − N2. The mixing process in the system under study was modeled at different initial carbon dioxide contents. To carry out a numerical experiment, a mathematical algorithm based on the D2Q9 model of lattice Boltzmann equations was used for modeling the flow of gases. We show that the model presented in the paper allows one to study the occurrence of convective structures at different heavy component contents (carbon dioxide). It has been established that in the system under study, the instability of the mechanical equilibrium occurs when the content of carbon dioxide in the mixture is more than 0.3 mole fractions. The characteristic times for the onset of convective instability and the subsequent creation of structural formations, the values of which depend on the initial content of carbon dioxide in the mixture, have been determined. Distributions of concentration, pressure and kinetic energy that allow one to specify the types of mixing and explain the occurrence of convection for a situation where, at the initial moment of time, the density of the gas mixture in the upper part of the diffusion channel is less than in the lower one, were obtained.

Lattice Boltzmann Method Pore-scale simulation of fluid flow and heat transfer in porous media: Effect of size and arrangement of obstacles into a channel

Lattice Boltzmann Method Pore-scale simulation of fluid flow and heat transfer in porous media: Effect of size and arrangement of obstacles into a channel

Darcy number influence on natural convection around porous cylinders in an enclosure using Darcy- Brinkman-Forchheimer model: LBM study

Darcy number influence on natural convection around porous cylinders in an enclosure using Darcy- Brinkman-Forchheimer model: LBM study

Simulation of fluid flow in a lid-driven cavity with different wave lengths corrugated walls using Lattice Boltzmann method

Simulation of fluid flow in a lid-driven cavity with different wave lengths corrugated walls using Lattice Boltzmann method

A simple one-step index algorithm for implementation of lattice Boltzmann method on GPU

A simple one-step index algorithm for implementation of lattice Boltzmann method on GPU

Hygrothermal simulation and risk evaluation - A literature review and assessment of the applicability of the Lattice Boltzmann Method to derive the influence of convection on moisture behaviour in building components

Since the Lattice Boltzmann Method (LBM) showed promising ways in describing fluid flow and convective phenomena, this literature review gives an overview of the application of LBM to date in the realm of hygrothermal simulations (HAM). Furthermore, ways to apply LBM to derive the influence of convection on moisture transport in building components are assessed. This is achieved by a literature review which is carried out for specific fields of application of LBM which are intertwined with topics of hygrothermal simulations (Natural convection, Porous media, Flow through channels). The introduction is accompanied by a condensed theoretical overview of the used LBM-scheme in most of the reviewed literature. It could be seen that, in regard to these topics, the majority of simulations is carried out 2-dimensionally using mostly the D2Q9 model with single relaxation times. The reviewed literature shows LBM as a validated tool, solidifying the choice of LBM for our purposes. No coupling of LBM to HAM-simulations to derive the influence of convection on moisture transport could be found. In conclusion, the deduction of parameters like the permeability is identified as a potent subfield for the coupling of LBM and HAM-simulations for further research.

SIMULATION OF TERNARY FLUID MIXTURES SEPARATION BY PHASE-FIELD FREE ENERGY LBM

This article reviews the mathematical and computer modeling of the process of ternary fluid mixture separation by free energy based phase flied Lattice Boltzmann method. The process under study is considered in a limited area having the shape of a rectangle. Three different sets of fluid components with different structures are specified. The mathematical model constructed to describe this process is based on the Navier-Stokes equation for an incompressible fluid and the Cahn-Hilliard equation. The numerical model is built on the basis of LBM using the D2Q9 model. Numerical experiments were performed for two scenarios: (1) – investigate the model without gravity, in order to determine the patterns of the surface tension effect and (2) - investigate the model with gravity force. The results obtained determine the adequacy of the constructed model for a three-component fluid.

Simulations of isotropic turbulent flows using lattice Boltzmann method with different forcing functions

Three different forcing functions are used with the lattice Boltzmann method (LBM) to simulate the forced isotropic turbulence in periodic boxes at different resolutions ranging from [Formula: see text] to [Formula: see text] grid points using the D3Q19 model. The aims of this study are to examine the effect of using different forcing functions on the LBM stability; to track the development of the turbulent fields at several resolutions, to investigate the effect of the weak compressibility due to change of fluid density on the flow simulations, and to identify the effective force type. The injection is performed through adding the force randomly to the collision term. The three forcing methods depend on sine and cosine as functions of the wave numbers and space. The forcing amplitude values of [Formula: see text] and the relaxation time [Formula: see text] are fixed in all cases. The single relaxation time model is found stable at such values of the forcing amplitude and the relaxation time. However, the development of the turbulent data at the different resolutions needs about 10000 time-steps to reach the required statistical state including clear visualizations of fine scale vortices. Many simulations have been tested using different values of the relaxation time [Formula: see text] and the development of the turbulent fields is found faster with fewer time-steps but the stability of the LBM is broken at some resolutions (not necessary the higher resolution). The statistical features of all fields, such as the Taylor and the Kolmogorov micro-scales, the Taylor Reynolds number, the flatness and the skewness, are calculated and compared with the previous efforts. The worm-like vortices are visualized at all cases and it is found that more fine vortices can be extracted as the resolution increases. The energy spectrum has a reasonable Kolmogorov power law at the resolutions of [Formula: see text] and [Formula: see text], respectively. Results show that the third forcing method that uses a cosine disturbance function has the best statistical features and the finest visualized vortical structures especially at higher resolutions. Extensive discussions about the density field and its evolution with time at different forcing functions, comparison to Navier–Stokes solutions and the time development of the energy spectra for all cases are also carried out.

LBM modeling of solid particle dynamics in a viscous medium

This article discusses the mathematical and computer modeling of single solid particle dynamics in a viscous medium. The results of the study were obtained using a 3D numerical algorithm implemented on the basis of the D3Q19 model of the lattice Boltzmann method (LBM). The moving «liquid-solid» interface is accounted for using an interpolated bounce back (IBB) scheme. The velocity of a solid particle motion and the trajectory of a particle at Re = 1,56 are obtained. The results are in good agreement with the experimental and numerical results of other authors.

Numerical study of geometric parameters effects on the suspended solid particles in the oil transmission pipelines

The innovation of this paper is geometric parameters effects of the oil transmission pipelines on the suspended solid particles. This geometry has been simulated with the Lattice Boltzmann Method based on D2Q9 model for analyzing solid particle tracing, streamlines, solid particle volume fraction, and nondimensional velocity field of fluid flow. These parameters have been investigated in 9 cases of the oil transmission pipelines at two different intensity of fluid flow. The results signified that maximum and minimum ranges of fluid velocity at [Formula: see text] were in case 3 that the oil transmission pipelines with diameter of the pipeline and bending radius, D and 2D, respectively. Also, maximum volume fraction of solid particles at bending radius at [Formula: see text] was in case 3 with diameter of the pipeline and bending radius, D and 2D, respectively. Also, in case 9, solid particles in the oil transmission pipelines were almost symmetrical. Finally, with comparison between figures of solid particles tracing and volume fraction of solid particles, by increasing of the diameter of oil transmission pipelines, the sediment of solid particles was decreased, also, by increasing of the bending radius of oil transmission pipelines, the sediment of solid particles was increased.

Numerical study on slip flow using the discrete unified gas-kinetic scheme

PurposeThis paper aims to explore the mechanism of the slip phenomenon at macro/micro scales, and analyze the effect of slip on fluid flow and heat transfer, to reduce drag and enhance heat transfer.Design/methodology/approachThe improved tangential momentum accommodation coefficient scheme incorporated with Navier’s slip model is introduced to the discrete unified gas kinetic scheme as a slip boundary condition. Numerical tests are simulated using the D2Q9 model with a code written in C++.FindingsVelocity contour with slip at high Re is similar to that without slip at low Re. For flow around a square cylinder, the drag is reduced effectively and the vortex shedding frequency is reduced. For flow around a delta wing, drag is reduced and lift is increased significantly. For Cu/water nanofluid in a channel with surface mounted blocks, drag can be reduced greatly by slip and the highest value of drag reduction (DR) (67.63%) can be obtained. The highest value of the increase in averaged Nu (11.78%) is obtained by slip at Re = 40 with volume fraction φ=0.01, which shows that super-hydrophobic surface can enhance heat transfer by slip.Originality/valueThe present study introduces and proposes an effective and superior method for the numerical simulation of fluid/nanofluid slip flow, which has active guidance meaning and applied value to the engineering practice of DR, heat transfer, flow control and performance improvement.

Mixed convection in an isosceles right triangular lid driven cavity using multi relaxation time lattice Boltzmann method

Mixed convection in an isosceles right triangular lid driven cavity using multi relaxation time lattice Boltzmann method

SIMULATION OF NUCLEATE BOILING BUBBLE BY THE PHASE-FIELD AND LATTICE BOLTZMANN METHOD

This article reviews the mathematical and computer modeling of the process of thermal phase transition in two-phase fluid flows. The nucleate boiling process is investigated in the presence of a constant heat source on a solid wall. Bubble formation and phase transition are taken into account. The flow characteristics and temperature distribution during nucleate boiling are obtained. The results of the numerical study were obtained using a 2D numerical algorithm implemented on the basis of the D2Q9 model of the Lattice Boltzmann method (LBM-Lattice Boltzmann method) and the phase field method. The calculations show that first the nucleation of a bubble is formed, then the bubble grows, breaks away from the boundary with the heat source, then, rising upward, undergoes deformation under the action of buoyancy forces. The effect of gravity and surface wettability on the bubble diameter during ascent is also numerically investigated. The results obtained are in good agreement with the experimental and numerical results of other authors.

Natural convection of nanofluids in solar energy collectors based on a two-phase lattice Boltzmann model

In order to improve the photothermal conversion efficiency of solar energy collectors, the laminar convection of nanofluids in five types of solar energy collectors was numerically studied with a two-phase lattice Boltzmann model. In the current simulation, Cu–water nanofluids (volume fraction φ = 0.3%) were chosen. The equilibrium distribution function with D2Q9 model and the boundary conditions of nonequilibrium extrapolation scheme were applied to establish the lattice Boltzmann model. The effects of different Rayleigh numbers (Ra = 104–106), structures (rectangle cavity, trapezoid cavity and parallelogram cavity) and aspect ratios (A = 2:1, 4:3 and 1:1) of solar energy collectors on the heat transfer were considered. The temperature distribution, streamline and entropy generation of nanofluids in the solar energy collectors were analyzed. Results demonstrated that the increase in Rayleigh number heightens the heat convection of nanofluids. The trapezoid cavity and parallelogram have a special structure, which will form a flow dead zone, weaken the heat transfer effect and determine the position of maximum entropy generation.

Axisymmetric lattice Boltzmann formulation for mixed convection with anisotropic thermal diffusion and associated bubble breakdown

The effect of the mixed convection with anisotropic thermal diffusion on the bubble breakdown inside a cylindrical cavity with a rotating top and the stationary bottom is investigated in this article. The lattice Boltzmann multiple relaxation time axisymmetric method with the D2Q9 model is used. The three distribution functions, one for axial and radial components of the velocity field, second for an azimuthal component of the velocity field, and third for the temperature field, are used. The code is validated for the fluid flow inside a lid-driven cylindrical cavity and for hot rotating-top-lid cylindrical cavity. The results are compared with the benchmark data. The effect of mixed convection on the Bödewadt boundary layer thickness and the temperature boundary layer thickness is investigated. The simulations are perfermed for various Reynolds number (Re) from of 990 and 2494, the Richardson number (Ri in 0.01 and 1, and Rayleigh number (Ra from 9801 and 6.22×106). This study concludes that the Bödewadt boundary layer thickness (δB) is ∝ to Ri and the temperature boundary layer thickness (δTc) is ∝ to Ri for 0.01≤ Ri ≤0.1. Further, the δB≈δTc for isotropic thermal diffusion. For an anisotropic thermal diffusion, the δB remains constant and δTc increases at Ri = 0.01 with an increase in the ratio of thermal diffusivity values (n). The bubble breakdown vanishes with an increase in Ri at a constant Re. The main application of this study is in the mixing/blending processes with convection inside cylindrical shaped reactors.