The lattice boltzmann equation for nonnewtonian fluid flow field. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of nonnewtonian fluids described by generalized newtonian models. Simplified lattice boltzmann method for nonnewtonian powerla w fluid flows. Construction of a nonnewtonian fluid model based on the. The lattice boltzmann method lindsay crowl introduction motivation ns equations blood flow. Pdf lattice boltzmann method for nonnewtonian power.
Lattice boltzmann method for nonnewtonian powerlaw fluids. Evaluating the capabilities of the lattice boltzmann. 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. Numerical simulation of nonnewtonian pseudoplastic fluid. 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. In this paper, we present a simplified lattice boltzmann method for non. Comparison of the finite volume and lattice boltzmann. The essence of the present method lies in the determination of sheardependent viscosity of the. A model of the lattice boltzmann method for nonnewtonian fluids was constructed. The fluid viscosity and the relaxation time parameter is completely decoupled. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of nonnewtonian fluids described by generalized. 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.
Unlike conventional numerical methods, the kinetic theory based lbm simulates fluid flows by tracking the evolution of the particle distribution function, and then. 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. A numerical method for incompressible nonnewtonian. 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. A lattice boltzmann approach for the nonnewtonian effect in. A comparison of nonnewtonian models for lattice boltzmann. The proposed solver has the second order of accuracy and can be applied on. Nonnewtonian models with shearthinning viscosity are commonly used to solve a variety of complex. 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. For the powerlaw model, only two constant parameters can cover shearthinning and shearthickening fluids. Third international conference on particlebased methods.
Nonnewtonian fluid flows, especially in three dimensions 3d, arise in numerous settings of interest to physics. Now, i want to elevate it by adding the ability to simulate the nonnewtonian fluids. During the last two decades great attention has been paid to the lattice boltzmann method lb. A multiplerelaxationtime lattice boltzmann flux solver for nonnewtonian power law fluid flows is proposed. A fortran code based on the lattice boltzmann method lbm was developed for this purpose. Electroosmotic flow of nonnewtonian fluid in microchannels. Lattice boltzmann method, nonnewtonian fluid, powerlaw model. Boltzmann models of fluid dynamics, which simulate newtonian fluids by simple interactions on the particle level. 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. Inexact newtontype methods for the solution of steady incompressible nonnewtonian flows with the supgpspg finite element formulation r. Accuracy of nonnewtonian lattice boltzmann simulations.
Latticeboltzmann method for nonnewtonian fluid flows. Simulation of fines migration using a nonnewtonian. The finite difference method was applied to discretize the lbm equations. Fines migration occurs in a block cave mine, and is characterised by the faster movement of fine and often lowgrade material.
Inexact newtontype methods for the solution of steady. Rbcs and platlets make it a collidal particle suspension. Latticeboltzmann methodfor nonnewtonian fluidflows susana gabbanelli. The present paper aims to study of nonnewtonian fluid flow behaviors in a two dimensional bifurcated channel using latticeboltzmann. The accuracy of the lattice boltzmann method for the simulation of nonnewtonian powerlaw fluids was investigated. Kinetic theory of nonlinear viscous flow in two and three dimensions m. Lattice boltzmann simulation of nonnewtonian powerlaw fluid. The shear stress of purely viscous but nonelastic nonnewtonian fluid is a function of shear rate only. A new numerical method for incompressible nonnewtonian. Numerical rheometry of nonnewtonian particle suspensions. Numerical investigation of the accuracy, stability, and.
Simulation of nonnewtonian fluid mixing using the lattice. I have already written a d2q9 lattice boltzmann code which uses immersed boundary method for complex geometries. Exact analytical solutions for two of these models have been derived and presented for a fully developed 2d channel flow. 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. A lattice boltzmann approach for the nonnewtonian effect. In the present paper, three nonnewtonian models for blood are used in a lattice boltzmann flow solver to simulate nonnewtonian blood flows. Summary in this paper, we present a simplified lattice boltzmann method for non.
The lattice boltzmann method has been studied and successively applied to modeling various. A laterally heated square enclosure, filled with air, was studied. Construction of a nonnewtonian fluid model based on the finite. Lbm is typically applied to simulate flow through a series of time steps, each consisting of streaming particle distributions to neighboring nodes and. Different numerical methods have been implemented to simulate internal natural convection heat transfer and also to identify the most accurate and efficient one. Abstract in the present study, the lattice boltzmann method lbm is applied to simulate the. The nonnewtonian behavior is embedded in the lbm through a dynamical change of the local relaxation time.
In fact, the lbm has been successfully applied to di. 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. 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.
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