Simulation of particle settling in rotating and non-rotating flows of non-Newtonian fluids

Abstract

In this paper finite element solutions are presented for the flow of Newtonian and non-Newtonian fluids around a sphere falling along the centreline of a cylindrical tube. Both rotating and stationary tube scenarios are considered. Calculations are reported for three different inelastic constitutive models that manifest shear-thinning, extension-thickening and their combination. The influence of inertia and these various forms of viscous response are examined for their influence upon the drag on the settling particle and the structure of the flow. Simulations are performed by employing a semi-implicit time marching Taylor-Galerkin/pressure-correction finite element algorithm, a fractional-staged scheme of secondorder accuracy. KEY WORDS Finite elements, Taylor-Galerkin/pressure correction, particle settling, drag, rotating and non-rotating flows, inelastic non-Newtonian fluids.

Computation of free surface flows with a Taylor-Galerkin/pressure-correction algorithm

“…Intrinsic to this study is the implementation of free surface location techniques. The numerical method is based upon a semi-implicit Taylor -Galerkin/pressure -correction finite element method (STGFEM) [1,2], which has been successfully implemented in a variety of different flow circumstances. Specific problems considered are stick-slip and die-swell flows under creeping conditions.…”

Particle Settling in a Non-Newtonian Fluid Medium Processed by Using the CEF Model

“…As an example to the application of the CEF fluid, we can consider the settling of small particles in a non-Newtonian fluid medium. The simulation of this problem according to the fluid mechanics principles may be realized by the flow of a non-Newtonian fluid around a sphere falling along the centerline of a cylindrical tube [9][10][11][12][13][14].…”

“…The flow domain is meshed using linear and quadratic triangular elements [9]. Three unstructured meshes are generated by an adaptive mesh generator, as given in Table 2 and shown in Figure 7.…”

“…In order to provide a basis for a comparison, and to pose the behavioral difference between inelastic and viscoelastic fluids, an example taken from the literature [9], for the simpler case υ 1 = 0, gives contours of streamfunction, velocity, stress, pressure and viscosity at parameter settings of n = 0.5 and We = Weissenberg number = 2.5 ( Figure 8). As it can be seen in the Figure 8, the flow accelerates as the fluid approaches the sphere.…”

A simple phenomenological non-Newtonian fluid model

“…However, for incompressible non-Newtonian liquids (for which the first invariant of the deformation rate tensor is zero) viscosity is usually considered to be a function of only the second and third principal invariants of the deformation rate tensor r) (IIQ, IIID) [3][4][5][6][7][8][9][10]. The main weakness of generalized Newtonian law model, in which the stress tensor is directly proportional to the deformation rate tensor through r] (IID, IIID), is its incapability to correctly represent the flow behavior in extensional flows, especially in plane flows, where the third invariant of deformation rate tensor IIID is 0.…”