A new numerical method for incompressible nonnewtonian. The lattice boltzmann method lindsay crowl introduction motivation ns equations blood flow. Exact analytical solutions for two of these models have been derived and presented for a fully developed 2d channel flow. Accuracy of nonnewtonian lattice boltzmann simulations.
The shear stress of purely viscous but nonelastic nonnewtonian fluid is a function of shear rate only. The lattice boltzmann method has been studied and successively applied to modeling various. Construction of a nonnewtonian fluid model based on the finite. Inexact newtontype methods for the solution of steady incompressible nonnewtonian flows with the supgpspg finite element formulation r. The nonnewtonian behavior is embedded in the lbm through a dynamical change of the local relaxation time. Kinetic theory of nonlinear viscous flow in two and three dimensions m. For the powerlaw model, only two constant parameters can cover shearthinning and shearthickening fluids. The lattice boltzmann method lbm is a numerical method based on computational statistical mechanics that is wellsuited for approximating complex flow behaviors such as nonnewtonian, free surface, and multiphase multicomponent flow. 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. Nonnewtonian fluid flows, especially in three dimensions 3d, arise in numerous settings of interest to physics. A fortran code based on the lattice boltzmann method lbm was developed for this purpose. Lattice boltzmann method for nonnewtonian powerlaw fluids. Nonnewtonian models with shearthinning viscosity are commonly used to solve a variety of complex. The essence of the present method lies in the determination of sheardependent viscosity of the.
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. The lattice boltzmann method lbm, a mesoscopic method between the molecular dynamics method and the conventional numerical methods, has been developed into a very efficient numerical alternative in the past two decades. The accuracy of the lattice boltzmann method for the simulation of nonnewtonian powerlaw fluids was investigated. To this end, simulation of nonnewtonian fluids with different flow behavior indices are conducted for different mach numbers and differently resolved lattices, both for the srt as well as the mrt collision model. We study an ad hoc extension of the latticeboltzmann method that allows the simulation of nonnewtonian fluids described by generalized newtonian models. Abstract in the present study, the lattice boltzmann method lbm is applied to simulate the. Construction of a nonnewtonian fluid model based on the. Rbcs and platlets make it a collidal particle suspension. Fines migration occurs in a block cave mine, and is characterised by the faster movement of fine and often lowgrade material. A numerical method for incompressible nonnewtonian.
Lbm is typically applied to simulate flow through a series of time steps, each consisting of streaming particle distributions to neighboring nodes and. A lattice boltzmann approach for the nonnewtonian effect in. Comparison of the finite volume and lattice boltzmann. Simulation of fines migration using a nonnewtonian. Summary in this paper, we present a simplified lattice boltzmann method for non. Electroosmotic flow of nonnewtonian fluid in microchannels. Third international conference on particlebased methods. A multiplerelaxationtime lattice boltzmann flux solver for nonnewtonian power law fluid flows is proposed. Numerical investigation of the accuracy, stability, and. The lattice boltzmann method computational fluid dynamics. Cascaded lattice boltzmann modeling and simulations of three. In fact, the lbm has been successfully applied to di. Numerical rheometry of nonnewtonian particle suspensions. A model of the lattice boltzmann method for nonnewtonian fluids was constructed.
We present a lb study of the flow of singlephase nonnewtonian fluids, using a power law relationship between the effective viscosity and the local shear rate. Latticeboltzmann methodfor nonnewtonian fluidflows susana gabbanelli. Lattice boltzmann method, nonnewtonian fluid, powerlaw model. The fluid viscosity and the relaxation time parameter is completely decoupled. Pdf lattice boltzmann method for nonnewtonian power. In the present paper, three nonnewtonian models for blood are used in a lattice boltzmann flow solver to simulate nonnewtonian blood flows. Now, i want to elevate it by adding the ability to simulate the nonnewtonian fluids. Boltzmann models of fluid dynamics, which simulate newtonian fluids by simple interactions on the particle level. The lb method has a remarkable ability to solve single phase, multiphase, single component, and multicomponent problems in complex geometries.
The lattice boltzmann equation for nonnewtonian fluid flow field. Simulation of nonnewtonian fluid mixing using the lattice. Different numerical methods have been implemented to simulate internal natural convection heat transfer and also to identify the most accurate and efficient one. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of nonnewtonian fluids described by generalized. Kinetic theory of nonlinear viscous flow in two and three.
The model is based on the recently introduced lattice. Inexact newtontype methods for the solution of steady. The proposed solver has the second order of accuracy and can be applied on. Evaluating the capabilities of the lattice boltzmann. In this paper, we present a simplified lattice boltzmann method for non. A decoupling multiplerelaxationtime lattice boltzmann. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of nonnewtonian fluids described by generalized newtonian models. The present paper aims to study of nonnewtonian fluid flow behaviors in a two dimensional bifurcated channel using latticeboltzmann. Since its origin, more than 15 years ago, the lattice boltzmann method lbm has proved to be a powerful numerical technique for the simulation of single and multiphase. During the last two decades great attention has been paid to the lattice boltzmann method lb.
Unlike conventional numerical methods, the kinetic theory based lbm simulates fluid flows by tracking the evolution of the particle distribution function, and then. The finite difference method was applied to discretize the lbm equations. A lattice boltzmann approach for the nonnewtonian effect. 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. We can derive the lattice boltzmann method from lattice gas automata by determining the probability that there is a particle moving in the ith direction at x,t. A comparison of nonnewtonian models for lattice boltzmann. Numerical simulation of nonnewtonian pseudoplastic fluid. A laterally heated square enclosure, filled with air, was studied.1135 219 1282 1104 1645 168 1260 279 36 1607 25 1 1623 941 577 158 1393 726 12 975 1056 1374 53 1529 454 1171 1034 1462 1118 1238 1645 153 34 1331 241 308 890 99 1320 537 561