Modelling of Power-law Fluid Flow Through Porous Media Using Smoothed Particle Hydrodynamics

Abstract

The flow of non-Newtonian fluids through two-dimensional porous media is analyzed at the pore scale using the smoothed particle hydrodynamics (SPH) method. A fully explicit projection method is used to simulate incompressible flow. This study focuses on a shear-thinning power-law model (n < 1), though the method is sufficiently general to include other stress-shear rate relationships. The capabilities of the proposed method are demonstrated by analyzing a Poiseuille problem at low Reynolds numbers. Two test cases are also solved to evaluate validity of Darcy's law for power-law fluids and to investigate the effect of anisotropy at the pore scale. Results show that the proposed algorithm can accurately simulate non-Newtonian fluid flows in porous media.

An incompressible SPH scheme with improved pressure predictions for free-surface generalised Newtonian flows

“…Many attempts have been made in the past to model inelastic non-Newtonian flows with both WCSPH [14][15][16][17][18][19] and ISPH [10,20,21]. The density invariance method of Shao and Lo [10] was the first ISPH methodology applied in non-Newtonian flows, and it has proven to be popular with other researchers, who adopted it in later works [17,[21][22][23].…”

The variational multiscale element free Galerkin method for the simulation of power-law fluid flows

“…(10) and then substituting a(x) back into Eq. (7), the MLS approximant can be defined as (13) where N(x) is the vector of MLS shape functions. Please refer to the book of Liu and Gu [2] in detail.…”

“…We get method were presented by Bell and Surana [15] and smoothed particle hydrodynamics were presented by Vakilha and Manzari [13]. The analytical solution of the velocity profile for a fully-developed laminar flow of a power-law fluid is given by…”

“…A detailed review on the meshless methods has been provided by Nguyen et al [1] and Liu and Gu [2]. Recently many meshless methods have been proposed and applied to computational fluid dynamics [3][4][5][6][7][8][9][10][11][12][13][14].…”

“…Subsequently, Zhang et al applied VMEFG to simulate the water wave problems [11] and MHD flow problems [12]. To the best of our knowledge, there are few published results when meshless method is used to non-Newtonian fluid flow problems and meshless method for the simulation of non-Newtonian are usually applied in collocation sets [13,14]. Although meshless collocation methods do not need background quadrature mesh and make the computation efficient, they may suffer from the accuracy and stability problems.…”