Construction Of A Non-Newtonian Fluid Model
Based On The Finite Difference Lattice
Boltzmann Method
Author(s)
S. Tajiri & M. Tsutahara
Abstract
A model of the lattice Boltzmann method for non-Newtonian fluids was
constructed. The shear stress of purely viscous but non-elastic non-Newtonian
fluid is a function of shear rate only. For the power-law model, only two constant
parameters can cover shear-thinning and shear-thickening fluids. Two power-law
models are introduced to the finite difference lattice Boltzmann method. One is a
model in which the collision parameter (the relaxation time) is determined as a
function of the shear rate, and then the viscosity changes point by point
according to the shear rate. For the other model, the effect of the variable
viscosity is introduced as an external force which is determined by the local
shear rate. Two-dimensional channel flow between two parallel plates was
calculated by using the above two models. Both models are shown to give
satisfactory results. However, some discontinuity appears in the calculation by
the former model that is due to instability of the calculation. For the latter model,
smooth velocity distributions are always obtained. The shear rate is estimated by
the second order and fourth order central finite difference scheme, but the
accuracy of the velocity distribution is to first order. A model in which the
normal stress can be introduced by the shear is being constructed in the same
manner. The normal stress was given by introducing the single mode Giesekus
constitutive model to the finite difference lattice Boltzmann method.
Keywords: finite difference lattice Boltzmann method (FDLBM), non-Newtonian
fluids, power-law model, Giesekus model.
Keywords
finite difference lattice Boltzmann method (FDLBM), non-Newtonian
fluids, power-law model, Giesekus model.
Related Book
Other papers in this volume
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