Influence of Coarse-Dispersive Solid Phase on the ‘Particles-Wall’ Shear Stress in Turbulent Slurry Flow with High Solid Concentration

Abstract

The paper concerns simulation of fully developed and axially-symmetrical turbulent flow of coarse-dispersive slurry if all solid particles have similar size and shape with particles diameter from 1 mm to 5 mm, solid density from 1045 kg/m 3 to 3000 kg/m 3 , and solid concentration by volume from 20% to 40%. The author examines the influence of particle diameter on additional shear stress due to the 'particles-wall' interactions for moderate and high solid concentration. The mathematical model was developed using Bagnold's concept, [26] and assumes that the total wall shear stresses are equal to the sum of 'liquid-wall' and 'particles-wall' shear stresses. The mathematical model was successfully verified with own measurements of frictional head loss in vertical coarse -dispersive slurry flow, named: 'sand-water', 'polystyrene-water' and 'pvc-water', [10], [26]. The mathematical model can predict 'particles-wall' shear stress, pressure drop and friction factor for coarse-dispersive turbulent slurry flow in a pipe, [10].The aim of the paper is to present qualitative and quantitative dependence of solid particle diameter, solid particle density, solid concentration, and Reynolds number for carrier liquid phase on the 'particles-wall' shear stress. It is demonstrated that the solid particle diameter plays crucial role in its dependence on the 'particleswall' shear stress. It was proved that in particular flow conditions the 'particles-wall' shear stress is much higher compared to the carrier liquid wall shear stress.

Improvements in the numerical prediction of fully-suspended slurry flow in horizontal pipes

“…The authors investigated the no-slip condition, the free-slip condition (i.e. zero wall shear stress), two partial slip boundary conditions [33,34], and the wall shear stress formulation of Bartosik [12]. They concluded that the solid phase noslip and free-slip boundary conditions are not appropriate for reproducing the flow configurations studied in this work, investigated experimentally by Shook and Bartosik [35].…”

“…A similar expression, accounting for the dependence upon λ only, was proposed by Gillies and Shook [10] some years later. Other and more recent correlations are those of Matousek [11], Gillies et al [7], and Bartosik [12]. It is worth noticing that the above mentioned formulas for τ w,p have been developed to be employed as part of physically-based models based on a global formulation for the estimation of the pressure gradient.…”

Settling Suspensions Flow Modelling: A Review

“…Recently these models have been employed in the study of turbulence modification for concentrated solid-liquid settling suspensions flow (Bartosik, 2011;Bartosik, 2010).…”

“…Earlier works derived a turbulent model that used the properties of the mixture for the calculations of settling suspension flow behavior (Roco & Shook, 1984). Two equations turbulence models (Wilcox, 2006) became increasingly popular in two-phase applications, and some recent works have employed this approach to highly concentrated solid-liquid settling suspension flows with turbulence modulation (Bartosik, 2010;Bartosik, 2011).…”

“…Searching the literature for current numerical studies trying to characterize on turbulence attenuation for solidliquid settling suspensions, some manuscripts are found where: drag correlations are modified in an attempt to reproduce experimental data where turbulence modulation occurs (Hadinoto, 2010;Hadinoto & Chew, 2010); singlephase Low Reynolds turbulence models are modified to incorporate turbulence modulation (Bartosik, 2010;Bartosik, 2011); Mixture Models with a Low Reynolds Turbulence closure for turbulence modulation in highly concentrated solid-liquid flows (Silva et al, 2013); EulerEuler model is used for pipe flow of concentrated slurries (Kaushal et al, 2012;Lahiri & Ghanta, 2010).…”