The lattice boltzmann method has been studied and successively applied to modeling various. The nonnewtonian behavior is embedded in the lbm through a dynamical change of the local relaxation time. Construction of a nonnewtonian fluid model based on the finite. A decoupling multiplerelaxationtime lattice boltzmann. Latticeboltzmann method for nonnewtonian fluid flows. Comparison of the finite volume and lattice boltzmann. Different numerical methods have been implemented to simulate internal natural convection heat transfer and also to identify the most accurate and efficient one. Numerical simulation of nonnewtonian pseudoplastic fluid. A new numerical method for incompressible nonnewtonian.
Inexact newtontype methods for the solution of steady. Summary in this paper, we present a simplified lattice boltzmann method for non. Simulation of nonnewtonian fluid mixing using the lattice. In the present paper, three nonnewtonian models for blood are used in a lattice boltzmann flow solver to simulate nonnewtonian blood flows. A numerical method for incompressible nonnewtonian. Cascaded lattice boltzmann modeling and simulations of three. Lattice boltzmann method, nonnewtonian fluid, powerlaw model. Construction of a nonnewtonian fluid model based on the. Numerical investigation of the accuracy, stability, and. During the last two decades great attention has been paid to the lattice boltzmann method lb. A model of the lattice boltzmann method for nonnewtonian fluids was constructed. 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. Lattice boltzmann simulation of nonnewtonian powerlaw fluid.
In section 3, the presented lbm model is validated for a pressuredriven nonnewtonian flow, and then numerical simulations of electroosmotic flow for nonnewtonian fluid are demonstrated and discussed. We study an ad hoc extension of the latticeboltzmann method that allows the simulation of nonnewtonian fluids described by generalized newtonian models. A lattice boltzmann approach for the nonnewtonian effect in. Abstract in the present study, the lattice boltzmann method lbm is applied to simulate the. In fact, the lbm has been successfully applied to di. A fortran code based on the lattice boltzmann method lbm was developed for this purpose. The accuracy of the lattice boltzmann method for the simulation of nonnewtonian powerlaw fluids was investigated. The fluid viscosity and the relaxation time parameter is completely decoupled. Boltzmann models of fluid dynamics, which simulate newtonian fluids by simple interactions on the particle level. Simplified lattice boltzmann method for nonnewtonian powerla w fluid flows.
The lattice boltzmann equation for nonnewtonian fluid flow field. Kinetic theory of nonlinear viscous flow in two and three. The lattice boltzmann method lindsay crowl introduction motivation ns equations blood flow. Kinetic theory of nonlinear viscous flow in two and three dimensions m. 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. 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. Exact analytical solutions for two of these models have been derived and presented for a fully developed 2d channel flow. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of nonnewtonian fluids described by generalized. Nonnewtonian models with shearthinning viscosity are commonly used to solve a variety of complex. Lattice boltzmann method for nonnewtonian powerlaw fluids.
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. 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. Nonnewtonian fluid flows, especially in three dimensions 3d, arise in numerous settings of interest to physics. Electroosmotic flow of nonnewtonian fluid in microchannels. The lb method has a remarkable ability to solve single phase, multiphase, single component, and multicomponent problems in complex geometries. The lattice boltzmann method computational fluid dynamics. Latticeboltzmann methodfor nonnewtonian fluidflows susana gabbanelli. Evaluating the capabilities of the lattice boltzmann. A multiplerelaxationtime lattice boltzmann flux solver for nonnewtonian power law fluid flows is proposed. 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. For the powerlaw model, only two constant parameters can cover shearthinning and shearthickening fluids. Accuracy of nonnewtonian lattice boltzmann simulations.
The shear stress of purely viscous but nonelastic nonnewtonian fluid is a function of shear rate only. Pdf lattice boltzmann method for nonnewtonian power. The model is based on the recently introduced lattice. A comparison of nonnewtonian models for lattice boltzmann. The present paper aims to study of nonnewtonian fluid flow behaviors in a two dimensional bifurcated channel using latticeboltzmann. 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. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of nonnewtonian fluids described by generalized newtonian models. Inexact newtontype methods for the solution of steady incompressible nonnewtonian flows with the supgpspg finite element formulation r. Fines migration occurs in a block cave mine, and is characterised by the faster movement of fine and often lowgrade material. Now, i want to elevate it by adding the ability to simulate the nonnewtonian fluids. 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. The proposed solver has the second order of accuracy and can be applied on.
Numerical rheometry of nonnewtonian particle suspensions. A lattice boltzmann approach for the nonnewtonian effect. A laterally heated square enclosure, filled with air, was studied. In this paper, we present a simplified lattice boltzmann method for non. The essence of the present method lies in the determination of sheardependent viscosity of the. Rbcs and platlets make it a collidal particle suspension. 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.
1599 710 1283 306 1108 573 477 1022 778 465 436 795 785 631 942 536 34 575 875 189 436 1189 271 1114 1012 1167 823 1328 1250 227 1166 449 1282 718 468 420 1013 800