the effect of the particle size distribution on non-newtonian turbulent ...

Chapter 2
2.14.2
Literature Review
Transition from Laminar to Turbulent Flow
Page 2.44
There are several methods in <strong>the</strong> literature to determine <strong>the</strong> transition between larninar and
turbulent flow. However, <strong>the</strong> full rheology should be used.
2.14.3 Turbulent flow
The Blasius type equations can be used to determine turbulent flow. However, most <strong>of</strong> <strong>the</strong>
work to develop semi-<strong>the</strong>oretical models for turbulent flow has centred around <strong>the</strong> mixing
length model <strong>of</strong> Prandtl. Hence, <strong>the</strong> logarithmic velocity <strong>distribution</strong> can be used to model
smooth wall Newtonian turbulent flow. A logarithmic velocity <strong>distribution</strong> with a roughness
function and a roughness Reynolds number to correlate <strong>the</strong> roughness function can be used
to model fully developed rough wall Newtonian turbulent flow. The Colebrook White
relation can be used to model partially rough wall Newtonian turbulent flow.
There are three approaches in <strong>the</strong> literature for modelling non-Newtonian turbulent flow data:
• empirical approach eg Bowen (1961),
• approach based on <strong>the</strong> slurry rheology eg Torrance (1963) or Wilson &
Thomas (1985, 1987),
• approach based on <strong>the</strong> <strong>particle</strong> <strong>effect</strong> or <strong>particle</strong> roughness <strong>effect</strong> eg Slatter
(1994).
The continuum approximation must be compromised as <strong>the</strong> solid <strong>particle</strong>s contained in <strong>the</strong>
slurry are large compared with <strong>the</strong> scale <strong>of</strong> modelling <strong>of</strong> <strong>the</strong> viscous sub-layer thickness.
Theoretical models must <strong>the</strong>refore account for <strong>the</strong> <strong>effect</strong> <strong>of</strong> <strong>the</strong> <strong>particle</strong>s in turbulent flow and
hence from <strong>the</strong> three possible approaches that can be adopted, <strong>the</strong> approach using <strong>the</strong> <strong>particle</strong>
roughness <strong>effect</strong> should be used. Although Bowen's method does produce good correlation
<strong>of</strong> non-Newtonian turbulent flow pipe data it cannot provide an explanation <strong>of</strong> <strong>the</strong> behaviour
<strong>of</strong> <strong>the</strong> slurry in terms <strong>of</strong> <strong>the</strong> physical properties <strong>of</strong> <strong>the</strong> slurry.
A wall roughness <strong>effect</strong>, <strong>particle</strong> <strong>effect</strong> or <strong>particle</strong> roughness <strong>effect</strong> has been reported in <strong>the</strong>
literature (Maude & Whitmore 1956, 1958, Mun 1988, Slatter 1994). This <strong>effect</strong> has been