Pdf lattice boltzmann method for nonnewtonian powerlaw. To have a lbe model for linear viscoelastic fluids nonnewtonian, you can look at the paper by p. The unstructured lattice boltzmann method for nonnewtonian flows. The nonnewtonian nature of the flow is implemented using a power law model. Nonnewtonian fluids on the other hand typically exhibit either shear thinning or shear thickening behaviour and in some cases, exhibit a yield stress, i. Unlike conventional numerical methods, the kinetic theory based lbm simulates fluid flows by tracking the evolution of the particle distribution function, and then. We study an ad hoc extension of the latticeboltzmann method that allows the simulation of nonnewtonian fluids described by. 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. Scribd is the worlds largest social reading and publishing site. Lattice boltzmann method and its applications in engineering. Here you will find the best books used in computational fluid dynamics, knowing the theory is extremely important to properly use any cfd software. At each lattice site, two new quantities are added. Simulation of non newtonian fluid mixing using the lattice boltzmann model james m.
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. The model employs the discrete element method dem to represent a range of particle geometries. 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. A comparison of nonnewtonian models for lattice boltzmann. 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. In the present paper, three non newtonian models for blood are used in a lattice boltzmann flow solver to simulate non newtonian blood flows.
Which is the best model of the lbm to apply for nonnewtonian fluid. Pdf lattice boltzmann method for nonnewtonian power. Although lbm has been widely applied in many areas, it is not stable or accurate in certain cases such as the nonnewtonian flow, fluids with. The shear stress of purely viscous but non elastic non newtonian fluid is a function of shear rate only. The classical latticeboltzmann scheme is extended in an attempt to represent viscoelastic fluids in two dimensions.
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. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of nonnewtonian fluids described by generalized. 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. Construction of a nonnewtonian fluid model based on the finite. Dec 10, 2009 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. 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. A directforcing immersed boundarynonnewtonian lattice boltzmann method ibnlbm with splitforcing scheme has been used to investigate the problem of particle sedimentation in shearthinning and shearthickening fluids. The terminal settling velocity is the most important factor, which affecting. The model is based on the recently introduced lattice. The present paper aims to study of nonnewtonian fluid flow behaviors in a two dimensional bifurcated channel using latticeboltzmann.
A lattice boltzmann approach for the nonnewtonian effect. This paper investigates the application of the lattice boltzmann model to non newtonian. Lattice boltzmann method fluid dynamics navierstokes. An improved multirelaxation time lattice boltzmann method for. Exact analytical solutions for two of these models have been derived and presented for a fully developed 2d channel flow. Proceedings of the third international conference on particlebased methods. Numerical rheometry of nonnewtonian particle suspensions. Kinetic theory of nonlinear viscous flow in two and three dimensions m. Simulation of nonnewtonian fluid mixing using the lattice. Sep 08, 2014 it is in order to maintain such fundamental conservation laws, and to reconcile them with the principle of relativity, which rests on the experiments of michelson and morley, and of bucherer, that we have adopted the principles of non newtonian mechanics. For the powerlaw model, only two constant parameters can cover shearthinning and shearthickening fluids.
This is used to enable the accuracy of the model to be assessed and is not a limitation of the model. Simulation of fines migration using a nonnewtonian lattice. How to simulate a nonnewtonian fluid with lattice boltzmann. In fact, the lbm has been successfully applied to di. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of non newtonian fluids described by generalized newtonian models. Construction of a nonnewtonian fluid model based on the.
There are a number of common rheology models or methods often used to characterise non newtonian fluids. Several textbooks have been written to address the need of students to learn about this relatively new method. Latticeboltzmann method for nonnewtonian fluid flows. 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 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. Studying the factors affecting the drag coefficient in non newtonian fluids 30 ijcpe vol. Lattice boltzmann method for nonnewtonian powerlaw fluids. The present method preserves the most desirable features of the lattice boltzmann and the immersed boundary methods. 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.
A model of the lattice boltzmann method for non newtonian fluids was constructed. We study an ad hoc extension of the latticeboltzmann method that allows the simulation of nonnewtonian fluids described by generalized newtonian models. Fines migration occurs in a block cave mine, and is characterised by the faster movement of fine and often lowgrade material. Summary in this paper, we present a simplified lattice boltzmann method for non. Buick university of new england physics and engineering armidale nsw australia joshua boyd university of new england physics and engineering armidale nsw australia abstract. Studying the factors affecting the drag coefficient in non. I have already written a d2q9 lattice boltzmann code which uses immersed boundary method for complex geometries. Evaluating the capabilities of the lattice boltzmann. Preface the lattice boltzmann method is increasingly attracting researchers in many areas from turbulence to multiphase flow in porous media. Nonnewtonian models with shearthinning viscosity are commonly used to solve a variety of complex.
Summary a new axisymmetric lattice boltzmann model is proposed for non. A secondorder accurate lattice boltzmann nonnewtonian. Now, i want to elevate it by adding the ability to simulate the non newtonian fluids. A secondorder accurate lattice boltzmann model is presented for nonnewtonian flow. Lattice boltzmann simulation of nonnewtonian powerlaw fluid. Kinetic theory of nonlinear viscous flow in two and three. A model of the lattice boltzmann method for nonnewtonian fluids was constructed. 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.
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