Lattice boltzmann simulation of droplet formation in nonnewtonian fluids article in communications in computational physics 1704. Endob adepartment of mechanical systems engineering, shinshu university 4171 wakasato, nagano 3808553, japan. Construction of a nonnewtonian fluid model based on the. Blood flow under various conditions of vessel is simulated as a non newtonian fluid by the twodimensional lattice boltzmann method, in which the casson model is used to express the relationship. Nonnewtonian models with shearthinning viscosity are commonly used to solve a variety of complex flow problems.
The lattice boltzmann method computational fluid dynamics. In cement3d printing, the fluids always exhibit according to the yielding behavior. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of nonnewtonian fluids described by generalized newtonian models. The incompressible lattice boltzmann equation can be used to simulate dense fluids as the algorithm can be shown to preserve the incompressible navierstokes equations that take the same form regardless of the fluid as long as it is newtonian but there exist even artificial fixes for non newtonian fluids, for incompressible gases as well as.
A lattice boltzmann model for nonnewtonian fluids was first introduced by aharonov and rothman 32 which was based on the powerlaw model and designed for two dimensional and steady flows. Pdf latticeboltzmann method for nonnewtonian fluid. Simple naviers slip boundary condition for the non. An efficient framework for fluidstructure interaction using. Yeomans research, which combines her expertise in statistical physics with the power of modern computers, is multifaceted, covering self assembly at molecular and macroscopic levels, drops moving in microchannels and on superhydrophobic surfaces, the rheology of highly non newtonian fluids such as liquid crystals, and most recently. Simulation of nonnewtonian fluid mixing using the lattice boltzmann model james m. Latticeboltzmann method for nonnewtonian fluid flows. Buick university of new england physics and engineering armidale nsw australia joshua boyd university of new england physics and engineering armidale nsw australia abstract. The power law model is used to represent the class of nonnewtonian fluids shearthinning and shearthickening.
An improved multirelaxation time lattice boltzmann method. May 25, 2012 read simulation of fines migration using a non. The efficiency of a stent is related to several parameters, including porosity and stent strut shapes. A lattice boltzmann study of the nonnewtonian blood flow. Lattice boltzmann simulation of nonnewtonian flow past. The lattice boltzmann method lbm of a nonnewtonian blood fluid is used.
Tsutahara graduate school of science and technology, kobe university, japan abstract a model of the lattice boltzmann method for nonnewtonian fluids was constructed. A new finitevolume discretization based upon an unstructured grid is used to integrate the differential form of the lattice boltzmann equation with a sheardependent viscosity, using a cellvertex finitevolume technique. Simulation of fines migration using a nonnewtonian lattice. Instead of solving the navierstokes equations directly, a fluid density on a lattice is simulated with streaming and collision relaxation processes. Sep 22, 2011 one of the alternatives for cfd simulation is the lattice boltzmann equation lbe, where the fluid is treated as fictitious mesoscopic particles not molecules. A secondorder accurate lattice boltzmann model is presented for nonnewtonian flow. Numerical rheometry of bulk materials using a power law fluid. A lattice boltzmann study of nonnewtonian flow in digitally.
In the present study, the lattice boltzmann method lbm is applied to simulate the flow of non newtonian shearthinning fluids in threedimensional digitally reconstructed porous domains. Boltzmann models of fluid dynamics, which simulate newtonian fluids by simple interactions on the particle level. A nonnewtonian direct numerical study for stationary and. Lbm theorie introduction classification topdown versus bottomup development cellular automata hpp, fhp and lga from lga to lbalbm comparison lbm in detail from boltzmann to.
The lattice boltzmann method is modified to allow the simulation of nonnewtonian sheardependent viscosity models. We study an ad hoc extension of the latticeboltzmann method that allows the simulation of nonnewtonian. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of non newtonian fluids described by generalized newtonian models. To improve the situation, a modified multirelaxationtime lattice boltzmann method was proposed. Numerical simulation of nonnewtonian pseudoplastic fluid. The goal of this paper is to identify numerically how the stent strut shape and the porosity affect the hemodynamics properties of the flow inside an aneurysm. The lattice boltzmann method introduction gunther brenner institute of applied mechanics clausthal university parcfd, antalya, 21 may 2007 2 contents part 1. Fines migration occurs in a block cave mine, and is characterised by the faster movement of fine and often lowgrade material.
Lattice boltzmann study of nonnewtonian blood flow in mother and daughter aneurysm and a novel stent treatment article in advances in applied mathematics and mechanics 62. A comparison of nonnewtonian models for lattice boltzmann. Blood flow under various conditions of vessel is simulated as a nonnewtonian fluid by the twodimensional lattice boltzmann method, in which the casson model is used to express the relationship. To set ideas, we first consider the pressure driven gaseous slip flow with small rarefaction through a long microchannel and formulate the problem in lb framework. The model incorporates the additional axisymmetric contributions into the. A model of the lattice boltzmann method for nonnewtonian fluids was constructed. Succi1 1iaccnr, viale del policlinico 7, 00161 roma, italy 2dept. Analysis of the casson and carreauyasuda nonnewtonian. An introduction for geoscientists and engineers, springer, heidelberg, 2006. Computational fluid dynamics cfd is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. A lattice boltzmann method based numerical scheme for. This method is an alternative to the conventional ones used in computational fluid mechanics, its programming is not complicated, and today it is applied to many. The lattice boltzmann method lbm is a numerical method based on computational statistical mechanics that is wellsuited for approximating complex flow behaviors such as non newtonian, free surface, and multiphase multicomponent flow. The nonnewtonian nature of the flow is implemented using a power law model.
Newtonian fluids with the lattice boltzmann method, acta geologica sinica english edition, 90, 3, 9991010, 2016. For the powerlaw model, only two constant parameters can cover shearthinning and shearthickening fluids. Computers are used to perform the calculations required to simulate the freestream flow of the fluid, and the interaction of the fluid liquids and gases with surfaces. According to the specific behavior of the fluids, it also has some shortcomings when applied to some special flow like as the non newtonian flow. The shear stress of purely viscous but non elastic non newtonian fluid is a function of shear rate only. Lattice boltzmann methods lbm, originated from the lattice gas automata lga method hardypomeaupazzis and frischhasslacherpomeau models, is a class of computational fluid dynamics cfd methods for fluid simulation. The flow past a series of tandem arrangement of two cylinders is computed in a confined domain. Pdf simulation of nonnewtonian blood flow by lattice. Coupled lattice boltzmann method and discrete element modelling of particle transport in turbulent fluid flows. Purpose the purpose of this paper is to present a novel computational framework based on the lattice boltzmann method lbm and discrete element method dem capable of simulating fines migration in three dimensions. Numerical investigation of the accuracy, stability, and. In this section you will find the most recommended books of computational fluid dynamics cfd, it is always necessary to have one or two reference books that help us understand the theory that involves a cfd software ansys cfx, ansys fluent, flow3d, openfoam, abaqus, etc. This geometry is made by two squared or trapezoid cavities at the bottom and top of the channel which can simulate an artery with local expansion. Lattice boltzmann simulation of droplet formation in non.
Coupled lattice boltzmann method and discrete element. The nonnewtonian part was modeled with a special forcing term. Read pressuredriven and electroosmotic nonnewtonian flows through microporous media via lattice boltzmann method, journal of nonnewtonian fluid mechanics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at. We extensively test the accuracy of the method for the case of shearthinning and shearthickening truncated powerlaw fluids in the parallel plate geometry, and show that the. The model is based on the recently introduced lattice. Here you will find the best books used in computational fluid dynamics, knowing the theory is extremely important to properly use any cfd software. Bingham fluid simulation in porous media with lattice. Conventional lattice boltzmann method lbm is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. In this paper, the powerlaw model for a nonnewtonian pseudoplastic flow is investigated numerically.
This book provides the first detailed survey of lbe theory and its major. This paper investigates the application of the lattice boltzmann model to nonnewtonian. Lbm was then utilized in conjunction with a powerlaw model to simulate shear thinning and shear thickening nonnewtonian fluid flows in parallel and reentrant geometries by drazer et al. A secondorder lattice boltzmann algorithm is used for powerlaw non newtonian flow simulation. In the current study, a directforcing immersed boundary nonnewtonian lattice boltzmann method ibnlbm is developed to investigate the sedimentation and interaction of particles in shearthinning and shearthickening fluids. Lattice boltzmann simulation of the flow of nonnewtonian. Simulation of nonnewtonian blood flow by lattice boltzman method. We use a lattice boltzmann lb kinetic scheme for modelling amphiphilic mixtures to impose couette flow on selfassembled gyroid mesophase. The non newtonian behavior is embedded in the lbm through a dynamical change of the local relaxation time. Pdf lattice boltzmann method for nonnewtonian powerlaw. A new axisymmetric lattice boltzmann model is proposed for non.
Lattice boltzmann simulations of slip flow of nonnewtonian. The lattice boltzmann method lindsay crowl introduction motivation ns equations blood flow model approaches origin lattice gas boltzmann equation conservation algorithm streaming step collision step bcs results simulations cooler simulations future directions navier stokes equations. Lattice boltzmann method for nonnewtonian and freesurface flow towards applications in wellbore cementing by matthewgrasinger bsincivilengineering,universityofpittsburgh,pittsburgh,pa. Introducing the lattice boltzmann method in a readable manner, this book provides detailed examples with complete computer codes. Nonnewtonian unconfined flow and heat transfer over a heated cylinder using the directforcing immersed boundarythermal lattice boltzmann method a. This book is an introduction to the theory, practice, and implementation of the lattice boltzmann lb method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. Numerical simulation of nonnewtonian pseudoplastic fluid in a microchannel using the lattice boltzmann method. Non newtonian fluids on the other hand typically exhibit either shear thinning or shear thickening behaviour and in some cases, exhibit a yield stress, i. The non newtonian part was modeled with a special forcing term. A lattice boltzmann model for nonnewtonian fluids was first introduced by aharonov and rothman which was based on the powerlaw model and designed for two dimensional and steady flows. In this paper, the extension of the technique to the simulation of non newtonian fluids is described.
An approximate equation relating the lattice boltzmann variable slip boundary condition with the macroscopic naviers slip boundary condition is proposed. The shear stress of purely viscous but nonelastic nonnewtonian fluid is a function of shear rate only. Numerical simulation of non newtonian pseudoplastic fluid in a microchannel using the lattice boltzmann method. The unstructured lattice boltzmann method for nonnewtonian flows. The model employs the discrete element method dem to represent a range of particle geometries. A practical introduction to the lattice boltzmann method. The lattice boltzmann method has been studied and successively applied to modeling various. The model is based on the recently introduced lattice gas and latticeboltzmann models of fluid.
This paper considers the application of lattice boltzmann method lbm to nonnewtonian flow in microfluidic devices. In this paper, we present a simplified lattice boltzmann method for non. In this work, a numerical study through the lattice boltzmann method lbm is carried out in order to investigate the behavior of twodimensional incompressible laminar non newtonian uid ows in a symmetric sudden expansion. Casson and carreauyasuda nonnewtonian blood viscosity models are implemented and are used to compare twodimensional newtonian and nonnewtonian flows in the context of simple steady flow and oscillatory flow in straight and curved pipe geometries. A lattice boltzmann model for non newtonian fluids was first introduced by aharonov and rothman 32 which was based on the powerlaw model and designed for two dimensional and steady flows. Numerical rheometry of bulk materials using a power law fluid and the lattice boltzmann method roger, owen. In the present work, the lattice boltzmann method was applied to a problem of the flow of a nonnewtonian binghamtype fluid between two plates, in the case of a poiseuille flow. An extrapolation method for wall and stent boundary conditions is used to resolve the characteristics of a highly complex flow.
Lattice boltzmann simulation of the flow of nonnewtonian fluids in porous media. We have gathered on this website several courses related to computational fluid dynamics cfd of various institutions and universities around the world totally free, we hope it is helpful and consultation for all students, engineers, professors and researchers who are passionate about cfd. The multirelaxation time lattice boltzmann method mrtlbm has an excellent performance in dealing with the complex flow in many different areas. We report evidence of nonnewtonian behaviour shear. In this section, you will also find books on other topics such as turbulent flow, naca airfoils, pumps, hydraulics, thermofluids, heat and mass transfer, aeronautics, fluid mechanics, etc. The fluid phase is captured using a non newtonian formulation of the lattice boltzmann method lbm and full hydrodynamic coupling of the lbm and dem is achieved using an immersed moving boundary condition 1, 2. Therefore, the lattice boltzmann method is of potential to simulate nonnewtonian. To ease the code development, a scientific programming strategy based on objectoriented concepts is developed.
In this study, the hybrid approach of immersed boundarynonnewtonian lattice boltzmann method ibnlbm is used to investigate the effects of a nonnewtonian fluid behavior, b the shape of immersed bodies, and c the number of forcing points used at the interface scheme on the accuracy of predicted hydrodynamic parameters. Technology, university parthenope, napoli, italy email. Lattice boltzmann study of nonnewtonian blood flow in. The d2q9 model of lattice boltzmann method is used to simulate the microchannel flow with expansion geometries. The proposed relation is validated both for the case of newtonian and nonnewtonian fluids. Statistical analysis of pulsating nonnewtonian flow in a. Pdf lattice boltzmann method for nonnewtonian power. Department of physics university of rome tor vergata.
Nonnewtonian models with shearthinning viscosity are commonly used to solve a variety of complex. The lattice boltzmann method has been established as an efficient technique for solving a wide range of complex problems in fluid dynamics including multiphase flows. In the present paper, three non newtonian models for blood are used in a lattice boltzmann flow solver to simulate non newtonian blood flows. The shear dependent behavior of the fluid is implemented through calculating the shear locally from the lattice distribution functions. There are a number of common rheology models or methods often used to characterise non newtonian fluids. Lattice boltzmann models for nonnewtonian flows ima. The unknown fields are placed at the nodes of the mesh and. A model of the lattice boltzmann method for non newtonian fluids was constructed. Evaluating the capabilities of the lattice boltzmann. A new twodimensional microscopic model is introduced for the simulation of nonnewtonian fluids.
Simulation of nonnewtonian fluid mixing using the lattice. Numerical rheometry of nonnewtonian particle suspensions. The nonnewtonian effect will result in a poor stability and accuracy when using standard lbm in the numerical simulation of yielding fluids. In the present work, the lattice boltzmann method was applied to a problem of the flow of a non newtonian binghamtype fluid between two plates, in the case of a poiseuille flow. Simulation of non newtonian fluid mixing using the lattice boltzmann model james m. Generalized latticeboltzmann equations progress in. It avoids the most complicated mathematics and physics without scarifying the basic fundamentals of the method. This is used to enable the accuracy of the model to be assessed and is not a limitation of the model. A numerical method for incompressible nonnewtonian. Clearly structured throughout, this book will be an invaluable. Pressuredriven and electroosmotic nonnewtonian flows. Lattice boltzmann method lbm is used to simulate the lid driven cavity flow to explore the mechanism of nonnewtonian fluid flow. We extensively test the accuracy of the method for the case of shearthinning and shearthickening truncated powerlaw. This paper considers the application of lattice boltzmann method lbm to non newtonian flow in microfluidic devices.
Nonnewtonian fluids on the other hand typically exhibit either shear thinning or shear thickening behaviour and in some cases, exhibit a yield stress, i. Scholarpedia the lattice boltzmann equation lbe is a minimal form of boltzmann kinetic equation which is meant to simulate the dynamic behaviour of fluid flows without directly solving the equations of continuum fluid mechanics. Exact analytical solutions for two of these models have been derived and presented for a fully developed 2d channel flow. There are a number of common rheology models or methods often used to characterise nonnewtonian fluids. A lattice boltzmann approach for the nonnewtonian effect in. Succi, the lattice boltzmann equation for fluid dynamics.
If you need something to make you sleepy, please read the short and concise, and free book. This paper investigates the application of the lattice boltzmann model to non newtonian. Unstructured lattice boltzmann method for nonnewtonian. Construction of a nonnewtonian fluid model based on the finite difference lattice boltzmann method s. The non newtonian effect will result in a poor stability and accuracy when using standard lbm in the numerical simulation of yielding fluids.
We extensively test the accuracy of the method for the case of shearthinning and. A lattice boltzmann approach for the nonnewtonian effect. Aug 23, 2012 lattice boltzmann schemes with relative velocities 30 april 2015 communications in computational physics, vol. Ahmadi is currently working on epa, doe and nasafunded projects for developing a new technique for modeling pollutant transport, dispersion and turbulent flows of dense and dilute, solidgas or liquid mixtures with application to coal transport and processing, spray formation, and hotgas filtration. A new lattice boltzmann approach within the framework of d2q9 lattice for simulating shearthinning nonnewtonian blood flows described by the powerlaw, carreauyasuda and casson rheology models is proposed in this study. In recent years, stylized forms of the boltzmann equation, now going by the name of lattice boltzmann equation lbe, have emerged, which relinquish most mathematical complexities of the true boltzmann equation without sacrificing physical fidelity in the description of many situations involving complex fluid motion. A lattice boltzmann study of the nonnewtonian blood flow in.