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

Chapter 2 Literature Review Page 2.16
At fixed values <strong>of</strong> T y , K and n, a root mean square error <strong>of</strong> fit function E can be defined for
a series <strong>of</strong> N data points in <strong>the</strong> laminar flow region,
E =
N - 1
2
(2.23)
The K value for minimum error K.u.. can be found by setting aE/aK=O for a fixed value <strong>of</strong>
Ty and n,
K. = 11
auo
T
2 y ]
+ l+n
The T y and n values are <strong>the</strong>n optimized to give a global minimum for E.
2.9 VELOCITY DISTRIBUTION FOR TURBULENT FLOW
n
(2.24)
Turbulent flow models for non-Newtonian fluids are normally based on <strong>the</strong> analytical
methods adopted for Newtonian fluid turbulent behaviour (eg. Torrance 1963, Wilson &
Thomas 1985, 1987, SIatter 1994). In this section turbulent flow for Newtonian fluids is
COvered although <strong>the</strong> <strong>effect</strong> <strong>of</strong> solid <strong>particle</strong>s is also considered as it is felt that this should
form part <strong>of</strong> <strong>the</strong> basis for turbulent flow analysis <strong>of</strong> any non-Newtonian flow model.
2.9.1 Wall Roughness
The type <strong>of</strong> turbulent flow encountered depends on <strong>the</strong> wall roughness (Govier & Aziz,
1972). Under microscopic investigation it can be seen that <strong>the</strong> inner wall <strong>of</strong> <strong>the</strong> pipe is not
smooth but many protrusions exist. The term wall, pipe or surface TOughness is used to
describe <strong>the</strong> complex <strong>size</strong>, shape and spacing <strong>of</strong> <strong>the</strong>se protrusions. The elttent <strong>of</strong> roughness
will depend on <strong>the</strong> material used in manufacturing <strong>the</strong> pipe and <strong>the</strong> method <strong>of</strong> its
manufacture. For a given fluid and velocity, roughness in a pipe increases <strong>the</strong> pressure drop