We study an ad hoc extension of the latticeboltzmann method that allows the simulation of non newtonian. Mechsys is a programming library for the implementation of simulation tools in mechanics. It is a discrete computational method based upon the boltzmann nist equation. An introduction to the lattice boltzmann method for. Construction of a nonnewtonian fluid model based on the. Lbm is typically applied to simulate flow through a series of time steps, each consisting of streaming particle distributions to. 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. Poiseuille flow and couette flow are calculated with the. This book provides the first detailed survey of lbe theory and its major.
An interpretation and derivation of the lattice boltzmann method using strang splitting paul j. Lattice boltzmann modelling sukop and thorne more broad, for applications the lattice boltzmann method, s. It is a discrete computational method based upon the boltzmann equation. A secondorder accurate lattice boltzmann nonnewtonian. Simulation of nonnewtonian fluid mixing using the lattice. 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.
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. A comparison of nonnewtonian models for lattice boltzmann. Numerical investigation of the accuracy, stability, and. Lattice boltzmann models for nonnewtonian flows ima. 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. There are a number of common rheology models or methods often used to characterise non newtonian fluids. Numerical simulations of nonnewtonian flow in a 2d channel show that these models predict different mass flux and velocity profiles even for the same. Latticegas cellular automata and lattice boltzmann models an introduction, wolfgardow, 2005. The fluid phase is captured using a nonnewtonian formulation of the lattice boltzmann method lbm and full hydrodynamic coupling of the lbm. For the powerlaw model, only two constant parameters can cover shearthinning and shearthickening fluids. I have already written a d2q9 lattice boltzmann code which uses immersed boundary method for complex geometries.
The lattice boltzmann method computational fluid dynamics. A secondorder accurate lattice boltzmann model is presented for non newtonian flow. In this paper, we present a simplified lattice boltzmann method for non. A computational model has been developed which facilitates the simulation of particle suspensions in nonnewtonian fluids.
Nonnewtonian models with shearthinning viscosity are commonly used to solve a variety of complex. In fact, the lbm has been successfully applied to di. Explain step in lattice boltzmann method computational. The present method preserves the most desirable features of the lattice boltzmann and the immersed boundary methods. I would recommend you to start of with some basics of statistical mechanics and the concept of cellular automata. We study an ad hoc extension of the lattice boltzmann method that allows the simulation of nonnewtonian fluids described by generalized. 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. Simulation of fines migration using a nonnewtonian. It has become an alternative and promising approach for the computational fluid dynamics problems lbm models the fluid as consisting of fictitious particles and such particles perform. Lattice boltzmann simulation of droplet formation in non. Fines migration occurs in a block cave mine, and is characterised by the faster movement of fine and often lowgrade material.
We extensively test the accuracy of the method for the case of shearthinning and shearthickening truncated powerlaw. Transport properties and time correlation functions, hardy et al, 1976. A nonslip boundary condition for lattice boltzmann simulations, to appear in phys. The non newtonian nature of the flow is implemented using a power law model. In the lattice boltzmann equation we are looking to add a similar term to incorporate a body force. The author did a great job in providing the necessary history of lattice boltzmann, from lattice gas cellular automaton, its subsequent development, and deployments to multiphase, supersonic, microfluidics, etc flows. 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. The lbm simpli es boltzmanns original idea of gas dynamics by reducing the number of particles and con ning them to the nodes of a lattice. 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. On boundary conditions in lattice boltzmann methods.
A nonuniform staggered cartesian grid approach for latticeboltzmann method v. In the present study, the lattice boltzmann method lbm is applied to simulate the flow of nonnewtonian shearthinning fluids in threedimensional digitally reconstructed porous domains. Theory of the lattice boltzmann method for multiphase and multicomponent fluids. On boundary conditions in lattice boltzmann methods physics of fluids 8, 2527 1996. Construction of a nonnewtonian fluid model based on the finite. Multiplerelaxationtime lattice boltzmann models in 3d.
Numerical rheometry of nonnewtonian particle suspensions. An hsv representation of nonnewtonian, latticeboltzmann ows robert geist, karl rasche, and james westall clemson university, clemson, south carolina, usa abstract an approach to modeling and visualization of nonnewtonian ows that is. An interpretation and derivation of the lattice boltzmann. Third international conference on particlebased methods.
His greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms such as mass, charge, and structure determine the physical properties of matter such. Lattice boltzmann simulation of the flow of non newtonian fluids in porous media. Pdf lattice boltzmann method for nonnewtonian power. A lattice boltzmann approach for the nonnewtonian effect. Actually i am reading a book about the lattice boltzmann methods, and here is a quotation. How to simulate a nonnewtonian fluid with lattice boltzmann. 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. The nonnewtonian behavior is embedded in the lbm through a dynamical change of the local relaxation time. Instead of solving the navierstokes equations directly, a fluid density on a lattice is simulated with streaming and collision relaxation. Books for theoretical understanding towards lbm, i would recommend the lattice boltzmann equation for fluid dynamics and beyon. We study an ad hoc extension of the latticeboltzmann method that allows the simulation of nonnewtonian fluids described by. In the present method unknown distribution functions at the wall are assumed to be an equilibrium distribution function with a counter slip velocity which is determined so that fluid velocity at the wall is equal to the wall velocity. The lattice boltzmann method is a powerful technique for the computational modeling of a wide variety of complex fluid flow problems including single and multiphase flow in complex geometries. Unlike conventional numerical methods, the kinetic theory based lbm simulates fluid flows by tracking the evolution of the.
This paper proposes a study of the computational efficiency of a lattice boltzmann model lbm solver to simulate the behavior of a generalized newtonian fluid. The lattice boltzmann equation for fluid dynamics and. Chapter 2 the boltzmann equation we have already seen1 that the dynamics of the boltzmann equation always mimimizes the h functional given by ht z dxdv fx,v,tlogfx,v,t. 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. Lattice boltzmann method for nonnewtonian powerlaw fluids. Although it can be shown that the lattice boltzmann equation is a finite difference form of the linearized continuous boltzmann equation 17, 18, we present rlbe as a selfcontained mathematical object representing a dynamical system with a finite number of moments in discrete space and time. Lara and jansson for parallel computing, showing a high mflups millions of fluid lattice updates per second ratio. The shear stress of purely viscous but nonelastic nonnewtonian fluid is a function of shear rate only. 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. February 20, 1844 september 5, 1906 was an austrian physicist and philosopher.
In this paper, the extension of the technique to the simulation of nonnewtonian fluids is described. The latticeboltzmann method introduction gunther brenner institute of applied mechanics clausthal university parcfd, antalya, 21 may 2007 2 contents part 1. Dellar ociam, mathematical institute, 2429 st giles, oxford, ox1 3lb, uk abstract the lattice boltzmann spacetime discretisation, as usually derived from. Latticeboltzmann method for nonnewtonian fluid flows. An introduction for geoscientists and engineers sukop, michael c. Lattice boltzmann simulation of droplet formation in nonnewtonian fluids article in communications in computational physics 1704. Summary in this paper, we present a simplified lattice boltzmann method for non. Multiplerelaxationtime lattice boltzmann simulation of non newtonian flows past a rotating circular cylinder keivan fallah, morteza khayat, mohammad hossein borghei, atena ghaderi and ehsan fattahi 1 jun 2012 journal of non newtonian fluid mechanics, vol. Since, however, the velocity of all the particles is constant in the lattice boltzmann model, we cannot simply introduce an expression with exactly the same form but must instead look to add a term that will modify the. Abstract in the present study, the lattice boltzmann method lbm is applied to simulate the. This book provides the first detailed survey of lbe. 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. The model employs the discrete element method dem to represent a range of particle geometries.
In recent years, certain forms of the boltzmann equationnow going by the name of lattice boltzmann equation lbehave emerged which relinquish most mathematical complexities of the true boltzmann equation without sacrificing physical fidelity in the description of complex fluid motion. Lattice boltzmann simulation of the flow of nonnewtonian. Latticeboltzmann methodfor nonnewtonian fluidflows susana gabbanelli. Therefore, the lattice boltzmann method is of potential to simulate non newtonian. Also, given the growing popularity of lbm, multiple tools 19, 7 have arisen which has consolidated this method into academia and industry. Original results for the use of the kl model in addition to the casson and carreauyasuda models are reported for nonnewtonian flow simulations using a lattice boltzmann lb flow solver. 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 model of the lattice boltzmann method for nonnewtonian fluids was constructed. The kinetic theory of gases the navierstokes equations for a newtonian. 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 nonuniform staggered cartesian grid approach for.