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

Chapter 2
2.11.1
Literature Review
The Dodge & Metzner Model
Page 2.28
The non-Newtonian turbulent flow model <strong>of</strong> Dodge & Metzner is probably <strong>the</strong> most quoted
and used <strong>of</strong> all flow models due to its simplicity and applicability to a wide range <strong>of</strong> non­
Newtonian fluids (Mun, 1988). The model was developed from <strong>the</strong> laminar flow work <strong>of</strong>
Metzner & Reed (1955) in which sixteen different non-Newtonian materials were studied.
Both Metzner & Reed (1955) and Dodge & Metzner (1958) stated that standard Newtonian
procedures could be used for turbulent flow predictions. In order to obtain a velocity pr<strong>of</strong>Ile
equation Dodge & Metzner a;sumed <strong>the</strong> existence <strong>of</strong>a discrete boundary layer (viscous sub­
layer), transition zone and turbulent core in <strong>the</strong> pipe. They also assumed that <strong>the</strong> apparent
flow behaviour index n' influences <strong>the</strong> point velocity in <strong>the</strong> turbulent core which means that
<strong>the</strong> turbulent flow head loss is dependant on n'.
Their relationship for turbulent flow is:
1
If = A. log
where
and
c =-
•
0,4
(n ')1.2
[ Re f{1 -.;:l] + c
MR n ,
(2.50)
(2.51)
(2.52)
From <strong>the</strong> assumptions made by Dodge & Metzner (1959) <strong>the</strong> above relationship will revert
to <strong>the</strong> smooth wall Newtonian model when n' = I. The above relationship can also be
represented graphically as shown in Figure 2.11.
2.11.2 The Torrance Model
Torrance developed a relationship between <strong>the</strong> fanning friction factor and <strong>the</strong> Reynolds
number for Herschel-BulkIey model fluids ie. <strong>the</strong> yield pseudoplastic rheological model.