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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
Chapter 2 Literature Review Page 2.45 supported by data from Park et al (1989) and Pokryvalio & Grozberg (1995). There are reported differences in <strong>the</strong> literature as to when <strong>the</strong> viscous sub-layer breaks down. Although <strong>the</strong> <strong>particle</strong> roughness <strong>effect</strong> has been reported in <strong>the</strong> literature <strong>the</strong>re is no published limit <strong>of</strong> <strong>the</strong> validity <strong>of</strong> <strong>the</strong> <strong>effect</strong>. 2.14.4 Objectives <strong>of</strong> Thesis Having reviewed <strong>the</strong> relevant literature <strong>the</strong> following areas for investigation can be noted: • There is a lack <strong>of</strong> published literature on <strong>the</strong> <strong>particle</strong> roughness <strong>effect</strong>. Slatter (1994) has developed a new general approach to turbulence flow modelling and concluded that <strong>the</strong> <strong>particle</strong> roughness <strong>effect</strong> was valid for <strong>the</strong> slurries that were tested. However, research is required to determine if Slatter's model is accurate with increasing <strong>particle</strong> <strong>size</strong> and whe<strong>the</strong>r <strong>the</strong> d 85 <strong>size</strong> (as suggested by Slatter) does produce a good representation <strong>of</strong> <strong>the</strong> <strong>particle</strong> roughness <strong>effect</strong>. • To investigate if <strong>the</strong> PSD does affect <strong>the</strong> turbulent flow behaviour <strong>of</strong> <strong>the</strong> slurry. • To determine if <strong>the</strong> correlation <strong>of</strong> Maude & Whitmore (<strong>the</strong> only o<strong>the</strong>r model to incorporate <strong>particle</strong> <strong>size</strong> besides <strong>the</strong> Slatter model) can accurately predict turbulent flow behaviour <strong>of</strong> non-Newtonian homogeneous slurries. • To determine if increasing <strong>particle</strong> <strong>size</strong> has an <strong>effect</strong> on turbulent flow behaviour. This can be achieved by using <strong>the</strong> <strong>the</strong>oretical models (as described in this chapter) to model experimental data and to observe and analyze any <strong>effect</strong>s <strong>particle</strong> <strong>size</strong> has on turbulent flow behaviour.
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THE EFFECT OF THE PARTICLE SIZE DIS
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Preamble DECLARATION Page iii I, Ga
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