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

Chapter 2 Literature Review Page 2.34
The area ratio A, is thus given by:
1 + :y n]
A
r
= 2 [ 0
1 + n '
and hence <strong>the</strong> viscous sub-layer thickness is:
(2.64)
(2.65)
where 0" and 0",. are equivalent Newtonian and non-Newtonian viscous sub-layer thicknesses
respectively.
The velocity <strong>distribution</strong> is given by:
u
-=251n
V. ' [ PV.y]
p.' + 5,5 + 11,6 (A, - 1) - 2,5 In(A,) .
The mean velocity is given by:
V V N
- = - + 11 6 (A - 1) - 2 5 In A - {}
V V' r ' r'
. .
where V N is <strong>the</strong> mean velocity for <strong>the</strong> equivalent Newtonian fluid and n is given by:
{} = -2,5 In [1 _T y ] _ 2,5 T y [1 + 0,5 T y ] •
To TO TO
2.11.5 The Slatter Model
(2.66)
(2.67)
(2.68)
As mentioned in Chapter 1 Slatter (1994) is one <strong>of</strong> <strong>the</strong> few researchers to have taken into
account <strong>the</strong> <strong>size</strong> <strong>of</strong> <strong>the</strong> <strong>particle</strong> contained in <strong>the</strong> fluid for turbulent flow analysis.
A new Reynolds number was developed for predicting <strong>the</strong> onset <strong>of</strong> turbulence. It was
modelled using <strong>the</strong> assumption that <strong>the</strong> unsheared plug present due to <strong>the</strong> yield stress acts as
a solid at <strong>the</strong> pipe axis and inhibits turbulence (Figure 2.14).