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

Chapter 5 Discussion Page 5.9
5.7 THEORETICAL MODELS
As stated Slatter's model was consistently <strong>the</strong> best model for <strong>the</strong> kaolin test sets and for
mixture 2 with increasing representative <strong>particle</strong> <strong>size</strong>. This is attributed to <strong>the</strong> fact that his
model is able to account for <strong>the</strong> roughness <strong>effect</strong> whereas <strong>the</strong> o<strong>the</strong>r models do not. Where
Slarter's model fails to predict <strong>the</strong> turbulent flow data <strong>of</strong> <strong>the</strong> mixture 1 test sets, it could be
for <strong>the</strong> following reasons. Firstly, it should be noted that <strong>the</strong> viscous sub-layer thickness is
relatively large in turbulent flow (± 300JLm) as opposed to <strong>the</strong> possible <strong>effect</strong>s <strong>of</strong> <strong>the</strong> pipe
and <strong>particle</strong> roughness <strong>effect</strong>s. In o<strong>the</strong>r words <strong>the</strong> viscous sub-layer is suppressing <strong>the</strong>
roughness <strong>effect</strong> and Slatter's model which is over predicting <strong>the</strong> shear stress values is over
compensating for a roughness <strong>effect</strong> which is not that significant. It is interesting to note for
<strong>the</strong> test data <strong>of</strong> <strong>the</strong> large pipes (ie. 200mm pipes) for mixture 1, when <strong>the</strong> roughness <strong>effect</strong>
could be a factor, <strong>the</strong> turbulent prediction <strong>of</strong> <strong>the</strong> Slatter model is fairly good - an average
percentage error <strong>of</strong>2.59%, 2,98% and 15,48% for <strong>the</strong> three tests. Also, from Table 5.1 it
can be seen that <strong>the</strong>re are relatively fewer larger <strong>particle</strong>s present in <strong>the</strong> viscous sub-layer
as opposed to <strong>the</strong> o<strong>the</strong>r test sets due to <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> viscous sub-layer (see section
5.5). Ano<strong>the</strong>r reason is that <strong>the</strong> rheology is tending towards being a Bingham plastic (ie. <strong>the</strong>
value for n is approaching n=l) and under <strong>the</strong>se conditions <strong>the</strong> Slatter model tends to over
predict <strong>the</strong> shear stress values. At high shear rate values for a Bingham plastic as opposed
to yield pseudoplastic <strong>the</strong> shear stress values will be greater as <strong>the</strong> viscous forces
predominate in this region for Bingham plastics.
Although Slatter's model is <strong>the</strong> best model overall. <strong>the</strong> data presented on <strong>the</strong> <strong>particle</strong>
rOughness <strong>effect</strong> (Figure 4.2) does bring into question <strong>the</strong> validity <strong>of</strong> <strong>the</strong> assumptions on
Which <strong>the</strong> Slatter model is based. However, because Slatter's model is based on <strong>the</strong> <strong>particle</strong>
roughness <strong>effect</strong> it proves very useful when undertaking for example scale-up from a smooth­
Walled small bore (eg. PVC pipe) to a rough wall large-scale pipe (eg. galvanised iron), or
Vice versa. Normally, for example, if <strong>the</strong> pressure drop in turbulent flow is predicted by <strong>the</strong>
sCale-up method <strong>of</strong> Bowen, a corrected pressure gradient would have to be estimated for <strong>the</strong>
change in roughness. This could be done by using <strong>the</strong> Govier & Aziz (1972) approach <strong>of</strong>
mUltiplying <strong>the</strong> predicted pressure gradient by a ratio <strong>of</strong> friction factors obtained from <strong>the</strong>